Composition operators and classical function theory

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Publication:1309670

zbMath0791.30033MaRDI QIDQ1309670

Joel H. Shapiro

Publication date: 6 December 1993

Published in: Universitext (Search for Journal in Brave)




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compactness of weighted composition operators on BMOACoposinormal Weighted composition operators on $H^{2}(\mathbb{D})$Essential norm of weighted composition followed and proceeded by differentiation operator from Bloch-type into Bers-type spacesSlice regular Besov spaces of hyperholomorphic functions and composition operatorsCommutants of composition operators induced by a parabolic linear fractional automorphisms of the unit diskJoint Carleson measure for the difference of composition operators on the polydisksNumerical range of weighted composition operators on the Fock spaceWeighted composition operators and differences of composition operators between weighted Bergman spacesApproximation numbers of composition operators on weighted besov spaces of analytic functionsFINITE SUM OF COMPOSITION OPERATORS ON FOCK SPACEFredholm composition operators on Hardy-Sobolev spaces with bounded reproducing kernelUnnamed ItemProduct-type operators on weak vector valued $\alpha$-Besov spacesCompact difference of composition operators on the Hardy spacesComposition operators on the Hardy–Hilbert space 𝐻² and model spaces 𝐾_{Θ}Thin Interpolating SequencesMaximal functions and properties of the weighted composition operators acting on the Korenblum, α-Bloch and α-Zygmund spacesComplex symmetric weighted composition operators on the Hardy spaceUnnamed ItemClosed range and cyclicity of composition operators on Hilbert spaces of entire functionsCOMPACT WEIGHTED COMPOSITION OPERATORS ON -SPACESInvertible weighted composition operatorsInvertible weighted composition operatorsCOMPACT DIFFERENCES OF COMPOSITION OPERATORSOn Stević-Sharma operators from weighted Bergman spaces to weighted-type spacesPath Connected Components in the Spaces of Weighted Composition Operators with the Strong Operator Topology IIInterpolating Blaschke products and angular derivativesEstimates of essential norm of generalized weighted composition operators from Bloch type spaces to nth weighted type 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operators and pull-back measure formulaDifference of weighted composition operatorsDigits and continuants in Euclidean algorithms. 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vector-valued Bloch spacesDifference of composition operators on the Bergman spaces over the ballSPECTRA OF LINEAR FRACTIONAL COMPOSITION OPERATORS ON THE GROWTH SPACE AND BLOCH SPACE OF THE UPPER HALF-PLANEOn the norm and the essential norm of weighted composition operators acting on the weighted Banach space of analytic functionsDynamics of weighted composition operators on function spaces defined by local propertiesUnnamed ItemNormal and isometric weighted composition operators on the Fock spaceThe Linear Fractional Model Theorem and Aleksandrov-Clark measuresUnnamed ItemOn a Li–Stević integral-type operator from Bloch-type spaces into logarithmic Bloch spacesAccesses to infinity from Fatou componentsNote on a class of k-paranormal weighted composition operators on the Fock space Fp(C)Monotone increment processes, classical Markov processes, and Loewner chainsProperties of solutions of integro-differential equations arising in heat and mass transfer theoryOn the rate of convergence 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(\mathbb{B}_n)\)Convergence of linear combinations of iterates of an inner functionComposition-differentiation operators on the Dirichlet spacePower bounded and power bounded below composition operators on Dirichlet type spacesA central limit theorem for inner functionsCompactification and decompactification by weights on Bergman spacesRelations of the class \(\mathcal{U}(\lambda )\) to other families of functionsConvexity of the Berezin rangeProduct-type operators on the space of fractional Cauchy transformsThe product operator between Bloch-type spaces of slice regular functionsLinear connection between composition operators on the Hardy spaceStević-Sharma operator on spaces of vector-valued holomorphic functions\(\mathcal{Q}_K\) spaces: a brief and selective surveySpectra of weighted composition operators with quadratic symbolsComposition operators on Hardy-Smirnov spacesClassifying simply connected wandering domainsDynamics of composition operators on Hilbert spaces of Dirichlet seriesLinear combination of composition operators on Bergman and Korenblum spacesPower bounded weighted composition operators and power bounded below composition operatorsComplex symmetric composition operators on the Newton spaceCompact double differences of composition operators on the Bergman spaces over the ballHilbertian Hardy-Sobolev spaces on a half-planeComposition operators on Hardy spaces of the homogenous rooted treesWeighted composition operators in functional Banach spaces: an axiomatic approachOn \(k\)-composition and \(k\)-Hankel composition operators on the derivative Hardy spaceSandwich weighted composition operators between some families of analytic functionsSupercyclicity criteria for \(C_0\)-semigroupsWeighted composition operators from Besov Zygmund-type spaces into Zygmund-type spacesComposition operator, boundedness, compactness, hyperbolic Bloch-type space \(\beta_\mu^*\), hyperbolic-type spaceComposition operators from weak to strong vector-valued Hardy spacesComposition operators on distinct Bergman spaces over planar domainsMatrix-valued Aleksandrov-Clark measures and Carathéodory angular derivativesComparison of singular numbers of composition operators on different Hilbert spaces of analytic functionsWeighted composition operator on quaternionic Fock spaceApproximation and entropy numbers of composition operatorsGeneralized composition operators from the Lipschitz space into the Zygmund spaceDifference of composition operators on spaces of vector-valued holomorphic functionsCompact difference of composition operators with smooth symbols on the unit ballTopological transitivity of shift similar operators on nonseparable Hilbert spacesBoundary vs. interior conditions associated with weighted composition operatorsCompact differences of composition operators on weighted Dirichlet spacesJoint Carleson measure and the difference of composition operators on \(A_\alpha^p(\mathbb{B}_n)\)Complex symmetric weighted composition operators on \(H^2(\mathbb{D})\)Composition as an integral operatorLindelöf's principle and estimates for holomorphic functions involving area, diameter or integral meansCompact composition operators with symbol a universal covering mapCarleson measures and embeddings of abstract Hardy spaces into function latticesComposition operators on the Lipschitz space of a treeBoundary regular fixed points in Loewner theoryGeneralized composition operators on Zygmund-Orlicz type spaces and Bloch-Orlicz type spacesOn complex symmetric operator matricesOn the Toeplitzness of the adjoint of composition operatorsWeighted composition followed and proceeded by differentiation operators from Zygmund spaces to Bloch-type spacesSome inequalities for the horosphere function and hyperbolically nonexpansive mappings on the Hilbert ballParabolic type semigroups: asymptotics and order of contactNecessary condition for compactness of a difference of composition operators on the Dirichlet spaceCarleson embeddings and some classes of operators on weighted Bergman spacesParabolic composition operators on the ballSemigroups of holomorphic functions and condenser capacityRepresentation theory in chiral conformal field theory: from fields to observablesCompact linear combination of composition operators on Bergman spacesThe products of differentiation and composition operators from logarithmic Bloch spaces to \(\mu \)-Bloch spacesTopological structure in the space of (weighted) composition operators on weighted Banach spaces of holomorphic functionsHypercyclicity of weighted composition operators on the weighted little Bloch spaceMean ergodic composition operators on generalized Fock spacesA note about the spectrum of composition operators induced by a rotationAn extremal composition operator on the Hardy space of the bidisk with small approximation numbersTopological and dynamical properties of composition operatorsOn boundedness and compactness of Toeplitz operators in weighted \(H^\infty\)-spacesSkew-symmetric and essentially unitary operators via Berezin symbolsLinear combination of two composition operators between different Fock spacesErgodic properties of composition operators on Banach spaces of analytic functionsComposition operators on some Banach spaces of harmonic mappingsThe iterates of composition operators on Banach spaces of holomorphic functionsHypercyclicity, supercyclicity, and cyclicity of a weighted composition operator on \(\ell^p\) spacesBounded composition operators and multipliers of some reproducing kernel Hilbert spaces on the bidiskSums of weighted differentiation composition operatorsWeighted composition operators on iterated weighted-type Banach spaces of analytic functionsProducts of weighted composition and differentiation operators into weighted Zygmund and Bloch spacesWeighted composition operators on the Hilbert space of Dirichlet seriesSpectral analysis of integrodifferential equations in Hilbert spacesOrthogonal decomposition of composition operators on the \(H^2\) space of Dirichlet seriesWeighted composition operators on the Fock spaceDifferences of composition operators followed by differentiation between weighted Banach spaces of holomorphic functionsLinear combinations of composition operators on \(H^{\infty }\) spaces over the unit ball and polydiskCompact differences of weighted composition operatorsContact points and Schatten class of composition operatorsThe double commutant property for composition operatorsWeighted Banach spaces of analytic functions with sup-norms and operators between them: a surveyPosinormal composition operators on \(H^2\)Carleson measures on Dirichlet type spaces in the quaternionic unit ballHypercyclic composition operators with automorphisms of the upper half-planeDenjoy-Wolff theory and spectral properties of weighted composition operators on \(\text{Hol}(\mathbb{D})\)Trace estimates of Toeplitz operators on Bergman spaces and applications to composition operatorsCompact intertwining relation for multiplication operators in several complex variablesOn similarity and commutant of a class of multiplication operators on the Dirichlet spaceWeighted composition operators on Hardy-Smirnov spacesComposition operators on the polydiscCompactness of composition operators on the Bergman spaces of convex domains and analytic discsComplex symmetric weighted composition operators on Bergman spaces and Lebesgue spacesGlobal integral criteria for composition operatorsWhich linear-fractional composition operators are essentially normal?Components of linear-fractional composition operators.On the Lipschitz continuity of the dilation of Bloch functionsAbsolutely summing Carleson embeddings on Hardy spacesCompact composition operators and Deddens algebrasSequences of weighted composition operators on the Hardy-Hilbert spaceA note on complex symmetric composition operators on the Bergman space \(A^2(\mathbb{D})\)Compactness of composition operators on a Hilbert space of Dirichlet seriesOn compactness of the difference of composition operatorsBackward-iteration sequences with bounded hyperbolic steps for analytic self-maps of the diskFrostman shifts of inner functionsGeneralized iterationMaximal cluster sets along arbitrary curvesSpectra of weighted composition operators on weighted Banach spaces of analytic functionsSimultaneous universalityTopological transitivity and mixing of composition operatorsAlgebraic and essentially algebraic composition operators on \(C(X)\)Toeplitz operators on harmonically weighted Bergman spaces and applications to composition operators on Dirichlet spacesAsymptotic \(T_u\)-Toeplitzness of weighted composition operators on \(H^2\)Hardy-Stein type identities and rate of growth of mean values of functions in generalized Hardy spacesDifference of composition operators between different Hardy spacesAntinormal weighted composition operatorsLocal spectral theory for invertible composition operators on \(H^ p\)Basic properties of multiplication and composition operators between distinct Orlicz spacesOn the Bergman space norm of the Cesàro operatorCompact composition operators between Bloch type spaces in the polydiskCompact and Hilbert-Schmidt differences of weighted composition operatorsDiscrete analogue of generalized Hardy spaces and multiplication operators on homogenous treesDirichlet spaces associated with locally finite rooted directed treesClosed range weighted composition operators on weighted Bergman spacesComposition operators on the discrete analogue of generalized Hardy space on homogenous treesAngular derivatives for holomorphic self-maps of the diskNorm-attaining weighted composition operators on weighted Banach spaces of analytic functionsEssential norms of composition operators between Bloch type spaces in the polydiskRigorous effective bounds on the Hausdorff dimension of continued fraction Cantor sets: A hundred decimal digits for the dimension of \(E_{2}\)Approximation numbers of composition operators on the Hardy space of the infinite polydiskEssential norms of weighted composition operators from weighted Bergman space to mixed-norm space on the unit ballInequalities for angular derivatives and boundary interpolationWeighted composition operators from the minimal Möbius invariant space into the Bloch spaceBounded composition operator on Lorentz spacesFredholm and semi-Fredholm composition operators on the small Bloch-type spacesEssential norm of the product of differentiation and composition operators between Bloch-type spacesComposition operators with a minimal commutantGeneralized composition operators on \(Q_{K,\omega} (p,q)\) spacesErratum to: ``Closed-range composition operators on \(\mathbb A^2\) and the Bloch spaceErratum to: ``Closed-range composition operators on weighted Bergman spacesWeighted composition operators between different Fock spacesDifference of weighted composition operators on the space of Cauchy integral transformsComposition operators in hyperbolic Bloch-type and \(F \left(p, q, s\right)\) spacesGeneralized composition operators from \(\mathcal{B}_\mu\) spaces to \(Q_{K, \omega}(p, q)\) spacesEigenfunctions of composition operators on Bloch-type spacesHypercyclic linear fractional composition operators on weighted Dirichlet spaces \(\mathcal{D}_\alpha^p\)A left linear weighted composition operator on quaternionic Fock spaceTopological structure of the set of composition operators on the weighted Bergman spaceBackward orbits and petals of semigroups of holomorphic self-maps of the unit discComposition operators with monomial symbol acting on weighted Hardy spacesDynamics and spectra of composition operators on the Schwartz spaceRigorous computation of diffusion coefficients for expanding mapsComplex symmetric weighted composition operators on \(\mathcal{H}_\gamma(\mathbb{D})\)Hypercyclic composition operators on the little Bloch space and the Besov spacesConvergence of powers of composition operators on certain spaces of holomorphic functions defined on the right half planeEssential norm of the composition operators on the general spaces \(H_{\omega,p}\) of Hardy spacesComplex symmetry of generalized weighted composition operators on Fock spacePath components of composition operators over the half-planeOn the rate of convergence of semigroups of holomorphic functions at the Denjoy-Wolff pointDifferences of weighted composition operators between the Fock spacesSubnormality of weighted shifts associated to composition operatorsComposition operators on Hilbert spaces of entire Dirichlet seriesWeighted composition operators on Korenblum type spaces of analytic functionsComposition operators between Hardy spaces on linearly convex domains in \(\mathbb{C}^2\)In Koenigs' footsteps: diagonalization of composition operatorsThe spectra of composition operators from linear fractional maps acting upon the Dirichlet spaceHypercyclic and chaotic convolution operators on Chébli-Trimèche hypergroupsSingular values and Schmidt pairs of composition operators on the Hardy spaceAlgebras of Toeplitz operators with oscillating symbolsNorms and spectral radii of composition operators acting on the Dirichlet spaceConvergent sequences of composition operatorsApproximation numbers of composition operators on the Dirichlet spaceThe conformal radius as a function and its gradient imageInterplay between complex symmetry and Koenigs eigenfunctionsThe numerical range of \(C^*_\psi C_\varphi\) and \(C_\varphi C^*_\psi\)Weighted composition-differentiation operators on the Hardy spaceAsymptotics and isometries of weighted composition operators on Banach spaces of holomorphic functionsClosed range composition operators on BMOAA mean counting function for Dirichlet series and compact composition operatorsWeighted composition operators on Fock spaces and their dynamicsOn weighted compositions preserving the Carathéodory classStrong transitivity of composition operatorsSums of weighted differentiation composition operators from weighted Bergman spaces to weighted Zygmund and Bloch-type spacesCyclic composition operators on smooth weighted Hardy spacesA new characterization of weighted composition operators from \(F(p, q, s)\) into Bloch type spaceExtended eigenvalues of composition operatorsComposition operators on a local Dirichlet space.Simply connected topological spaces of weighted composition operatorsA general view of multipliers and composition operatorsInner functions and cyclic composition operators on \(H^2(B_n)^1\).The numerical ranges of automorphic composition operatorsWhen is zero in the numerical range of a composition operator?Joint hyponormality of composition operators with linear fractional symbols.On Volterra composition operators from Bergman-type space to Bloch-type spaceUniversal families and hypercyclic operatorsComposition operators on weighted Bergman-Orlicz spacesProperties of analytic Morrey spaces and applicationsde Branges–Rovnyak Spaces and Norm-Constrained InterpolationA note about Volterra operators on weighted Banach spaces of entire functionsSome integral-type operators from F(p,q,s) spaces to mixed-norm spaces on the unit ballRogosinski's lemma for univalent functions, hyperbolic Archimedean spirals and the Loewner equationNormal and Cohyponormal Weighted Composition Operators on H 2New characterizations for weighted composition operator from Zygmund type spaces to Bloch type spacesSemigroup-fication of univalent self-maps of the unit discSupercyclic composition \(C_0\)-semigroupsComponents of the space of weighted composition operators between different Fock spaces in several variablesSpectra of composition operators on the Dirichlet space induced by full-maps of the diskProduct-type operators from general space \(F(p,q,s)\) to \(\mu\)-Bloch spaces on the unit ball in \(\mathbb{C}^n\)Fejér-type positive operator based on Takenaka-Malmquist system on unit circleGeometric Julia-Wolff theorems for weak contractionsProduct-type operators on a class of Banach spaces of analytic functions into \(\mu\)-Bloch spaces on the unit ball in \(\mathbb{C}^n\)Real symmetric, unitary, and complex symmetric weighted composition operators on Bergman spaces of polydiskComposition operators on weighted analytic spacesWeighted composition operators on Bergman spaces Aωp$A^p_\omega$On the selfcommutator of automorphic composition operatorsSuperconvergence and regularity of densities in free probabilityIsolation amongst composition operators on L^p(μ)-spaces (1 ≤ p ≤ ∞)Order boundedness and essential norm of generalized weighted composition operators on Bergman spaces with doubling weightsTopological structure of the space of composition operators on \(L^{\infty}\) of an unbounded, locally finite metric spaceConformal invariants and the angular derivative problemComposition operators on weighted Hilbert spaces of Dirichlet seriesDifference of composition operators on the weighted Bergman spaces over the half-planeAdmissibility and Observability of Jeffreys Type of Overdamped Second Order Linear SystemsDIFFERENCES OF COMPOSITION OPERATORS BETWEEN WEIGHTED BANACH SPACES OF HOLOMORPHIC FUNCTIONSNonlinear resolvents and decreasing Loewner chainsOn compositional dynamics on hardy spaceComposition operators on Fock-type spacesProduct-type operators on Banach spaces of analytic functions on the upper half-planeComplex symmetric weighted composition operators on weighted Hardy spaceDenjoy-Wolff points on the bidisk via modelsUniversal composition operators on weighted Dirichlet spacesInvestigation of integro-differential equations by methods of spectral theoryComposition operators with universal translates on \({S^2}(\mathbb{D})\)Spectral properties of weighted composition operators on Hol(\mathbb{D}) induced by rotationsDifference of weighted composition operators over the ballWeighted differentiation composition operator from logarithmic Bloch spaces to Bloch-type spacesAbsolutely summing Carleson embeddings on Bergman spacesToeplitz operators and composition operators on the \(q\)-Bergman spaceCompact weighted composition operators on the Hardy spaceMean growth of Koenigs eigenfunctionsSelf-commutators of automorphic composition operators on the Dirichlet spaceUnnamed ItemUnnamed ItemUnnamed ItemUnnamed ItemUnnamed ItemCONTINUITY OF WEIGHTED COMPOSITION OPERATORS BETWEEN WEIGHTED BLOCH TYPE SPACESTHE HILBERT–SCHMIDT NORM OF A COMPOSITION OPERATOR ON THE BERGMAN SPACEIsometric weighted composition operators on weighted Banach spaces of type $H^\infty }$Linear combinations of composition operators on weighted Dirichlet spacesRestriction theorems for Hankel operatorsDIFFERENCES OF COMPOSITION OPERATORS BETWEEN WEIGHTED BERGMAN SPACES AND WEIGHTED BANACH SPACES OF HOLOMORPHIC FUNCTIONSCOMPOSITION OPERATORS BELONGING TO SCHATTEN CLASS 𝒮pToeplitz-composition $C^{*}$-algebras for certain finite Blaschke productsAngular derivatives at boundary fixed points for self-maps of the diskEssential norms of composition operators between Bloch type spacesComposition operators on a Banach space of analytic functionsFactorization of singular integral operators with a Carleman shift via factorization of matrix functions: the anticommutative caseJoint spectrum of subnormal $n$-tuples of composition operatorsCompact composition operators on Besov spacesGeometric description of the classification of holomorphic semigroupsSpectra of some invertible weighted composition operators on Hardy and weighted Bergman spaces in the unit ballNevanlinna counting function and pull–back measureComplex symmetry of weighted composition operators in several variablesWeighted Composition Operators on Weighted Banach Spaces of Holomorphic Functions on the Unit Polydisk with Closed RangeEssential norm of the difference of composition operators on Bloch spaceIsometric composition operators on weighted Dirichlet spaceOrbits of Cesàro type operatorsIsometric equivalence of isometries on 𝐻^{𝑝}Differences of weighted composition operators acting from Bloch space to 𝐻^{∞}Norms of linear-fractional composition operatorsBELLWETHERS FOR BOUNDEDNESS OF COMPOSITION OPERATORS ON WEIGHTED BANACH SPACES OF ANALYTIC FUNCTIONSCompact composition operators on BMOA and the Bloch spaceJulia theory for slice regular functionsSemigroups of composition operators on Hardy spaces of the half-planeMultiplication operators on S2($$\mathbb{D}$$)A note on composition operators acting on holomorphic Sobolev spacesBloch-to-BMOA compositions on complex ballsPath connected components in weighted composition operators on $h^\infty $ and $H^\infty $ with the operator normCyclicity of the adjoint of weighted composition operators on the hilbert space of analytic functionsTopological mixing and Hypercyclicity Criterion for sequences of operatorsIsometries of the Bloch space among the composition operatorsComposition operators on spaces of entire functionsLinear subsets of nonlinear sets in topological vector spacesCritical Points, the Gauss Curvature Equation and Blaschke ProductsProducts of differentiation, composition and multiplication from Bergman type spaces to Bers type spacesHypercyclic operators that commute with the Bergman backward shiftComposition operators on Dirichlet-type spacesSpectral theory and hypercyclic subspacesDifferences of generalized weighted composition operators between growth spacesHankel operators from the space of bounded analytic functions to the Bloch spaceCompact Composition Operators on BMOAComposition operators on some Möbius invariant Banach spacesThe range of linear fractional maps on the unit ballThe Nevanlinna counting functions for Rudin’s orthogonal functionsFixed points of commuting holomorphic mappings other than the Wolff pointEstimates of Norm and Essential norm of Differences of Differentiation Composition Operators on Weighted Bloch SpacesComposition operators with linear fractional symbols on vector-valued Bergman spacesApproximation numbers of composition operators on the Hardy and Bergman spaces of the ball and of the polydiskLIMITS OF FRACTIONAL DERIVATIVES AND COMPOSITIONS OF ANALYTIC FUNCTIONSMultifractal vector fields and stochastic Clifford algebraTHE ESSENTIAL NORMS OF COMPOSITION OPERATORS ON WEIGHTED DIRICHLET SPACESDifference of generalized integration operators on the space of Cauchy transformsProblems on Weighted and Unweighted Composition OperatorsComposition operators between Bergman and Hardy spacesHardy spaces and twisted sectors for geometric modelsComplex symmetric weighted composition operatorsDifferences of weighted composition operators from hardy space to weighted-type spaces on the unit ballHypercyclic composition operators on Hv0‐spacesA brief note on compactness of composition operators on H2Difference of Differentiation Composition Operators on the Fractional Cauchy Transforms SpacesEssential normality for certain finite linear combinations of linear-fractional composition operators on the Hardy space H 2Hyperbolic composition operators on the ballSubnormal semigroups of composition operatorsCompact Composition Operators on the Bloch SpaceComposition operators on Banach function spacesOn a Parametrization Formula for the Solution Set of a Completely Indeterminate Generalized Matricial Carathéodory-Fejér ProblemToeplitzness of composition operators on a Hilbert space of Dirichlet seriesCompactification, and beyond, of composition operators on Hardy spaces by weightsUnnamed ItemNuclear composition operators on Bloch spacesUnnamed ItemAsymptotic behavior of the powers of composition operators on Banach spaces of holomorphic functionsComplex symmetric weighted composition operators on the spaceUnnamed ItemGeneralized Volterra operators on polynomially generated Banach spacesSpectra of composition operators on Fock-type spacesInterpolating sequences for weighted Bergman spaces on strongly pseudoconvex bounded domainsGENERALISED WEIGHTED COMPOSITION OPERATORS ON BERGMAN SPACES INDUCED BY DOUBLING WEIGHTSIsometric composition operators for the Möbius invariant Hp norm of BMOA