Operator theory on noncommutative domains

DOI10.1090/S0065-9266-09-00587-0zbMath1194.47001arXivmath/0703062MaRDI QIDQ3560924

Gelu Popescu

Publication date: 17 May 2010

Published in: Memoirs of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0703062

zbMATH Keywords

interpolationcharacteristic functioninvariant subspaceCauchy transformcurvaturedilationmodel theoryFock spaceweighted shiftsfunctional calculuscommutant liftingvon Neumann inequalityPoisson transformWold decompositionfree holomorphic functionHardy algebramultivariable operator theorynoncommutative varietyBohr inequalitynoncommutative domain

Mathematics Subject Classification ID

Spaces of vector- and operator-valued functions (46E40) Several-variable operator theory (spectral, Fredholm, etc.) (47A13) Functional calculus for linear operators (47A60) Operator spaces and completely bounded maps (46L07) Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones) (47A56) Linear operator methods in interpolation, moment and extension problems (47A57) Dilations, extensions, compressions of linear operators (47A20) Research exposition (monographs, survey articles) pertaining to operator theory (47-02) Noncommutative function spaces (46L52) Representation theory of linear operators (47A67)

Related Items (44)

Euler characteristic on noncommutative polyballs ⋮ Operator theory on noncommutative polydomains. I. ⋮ Matricial function theory and weighted shifts ⋮ Multivariable Beurling–Lax representations: the commutative and free noncommutative settings ⋮ Characteristic functions and functional models on noncommutative varieties ⋮ Free holomorphic functions on the unit ball of \(B(\mathcal H)^n\). II ⋮ An Introduction to Hilbert Module Approach to Multivariable Operator Theory ⋮ Function theory from tensor algebras ⋮ Interpolation and commutant lifting with weights ⋮ Representations of \(C^*\)-algebras associated with noncommutative polyvarieties ⋮ Bohr inequalities on noncommutative polydomains ⋮ Operator theory on noncommutative polydomains. II ⋮ Operator theory on noncommutative varieties in polydomains ⋮ Invariant subspaces for certain tuples of operators with applications to reproducing kernel correspondences ⋮ Noncommutative varieties, symmetric weighted Fock spaces, and multipliers ⋮ Factorizations of characteristic functions of iterated liftings ⋮ Non-commutative holomorphic functions on operator domains ⋮ Noncommutative multivariable operator theory ⋮ Doubly \(\Lambda\)-commuting row isometries, universal models, and classification ⋮ Brerezin kernels and Wold decompositions associated with noncommutative polydomains ⋮ Joint similarity in admissible noncommutative polydomains ⋮ Free biholomorphic functions and operator model theory. II ⋮ Berezin transforms on noncommutative varieties in polydomains ⋮ Classification of noncommutative domain algebras ⋮ Similarity problems in noncommutative polydomains ⋮ Crossed Products of Operator Algebras ⋮ Bergman spaces over noncommutative domains and commutant lifting ⋮ Bohr inequalities for free holomorphic functions on polyballs ⋮ Noncommutative hyperballs, wandering subspaces, and inner functions ⋮ Brown-Halmos characterization of multi-Toeplitz operators associated with noncommutative polyhyperballs ⋮ Hyper-positive definite functions I: scalar case, branching-type stationary stochastic processes ⋮ Free holomorphic functions on the noncommutative polydomains and universal models ⋮ Bohr radii of vector valued holomorphic functions ⋮ Invariant subspaces and operator model theory on noncommutative varieties ⋮ Berezin transforms on noncommutative polydomains ⋮ Holomorphic functions on the quantum polydisk and on the quantum ball ⋮ Ergodic actions of convergent Fuchsian groups on quotients of the noncommutative Hardy algebras ⋮ Noncommutative hyperbolic geometry on the unit ball of \(B(\mathcal H)^n\) ⋮ Multi-Toeplitz operators and free pluriharmonic functions ⋮ Constrained characteristic functions, multivariable interpolation, and invariant subspaces ⋮ Cyclic row contractions and rigidity of invariant subspaces ⋮ Weighted Cuntz-Krieger algebras ⋮ Curvature invariant on noncommutative polyballs ⋮ Toeplitz corona and the Douglas property for free functions

Cites Work

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• On a bitangential interpolation problem for contractive-valued functions on the unit ball
• Hardy algebras, \(W^*\)-correspondences and interpolation theory
• Every completely polynomially bounded operator is similar to a contraction
• Models for n-tuples of noncommuting operators
• Characteristic function of a pure commuting contractive tuple
• Canonical models for representations of Hardy algebras
• On CNC commuting contractive tuples
• Noncommutative convexity arises from linear matrix inequalities
• Free holomorphic functions on the unit ball of \(B(\mathbb H)^n\)
• The Arveson extension theorem and coanalytic models
• Models for noncommuting operators
• The commutant lifting approach to interpolation problems
• Interpolation of rational matrix functions
• On intertwining dilations for sequences of noncommuting operators
• On a quotient norm and the Sz.-Nagy-Foias lifting theorem
• Nevanlinna-Pick interpolation for non-commutative analytic Toeplitz algebras
• Tensor algebras over \(C^*\)-correspondences: Representations, dilations, and \(C^*\)-envelopes
• Interpolation problems in several variables
• Subalgebras of \(C^*\)-algebras. III: Multivariable operator theory
• Poisson transforms on some \(C^*\)-algebras generated by isometries
• Metric constrained interpolation, commutant lifting and systems
• The algebraic structure of non-commutative analytic Toeplitz algebras
• Multivariable Nehari problem and interpolation.
• Complete Nevanlinna-Pick kernels
• Central intertwining lifting, suboptimization, and interpolation in several variables
• An operator-valued Poisson kernel
• ``Positive noncommutative polynomials are sums of squares.
• Realization and interpolation for Schur--Agler-class functions on domains with matrix polynomial defining function in \(\mathbb C^{n}\)
• Factorization and reflexivity of Fock spaces
• Functional calculus for noncommuting operators
• Multi-analytic operators on Fock spaces
• Noncommutative interpolation and Poisson transforms
• Characteristic functions for multicontractions and automorphisms of the unit ball
• Noncommutative Berezin transforms and multivariable operator model theory
• Characteristic function for polynomially contractive commuting tuples
• Characteristic functions and joint invariant subspaces
• Matrix representations for positive noncommutative polynomials
• Subalgebras of \(C^ *\)-algebras
• On two problems concerning linear transformations in Hilbert space
• The structure of free smigroup algebras
• Isometric Dilations of Non-Commuting Finite Rank n-Tuples
• Spherical contractions and interpolation problems on the unit ball
• Isometric Dilations for Infinite Sequences of Noncommuting Operators
• ON BOHR'S INEQUALITY
• Entropy and multivariable interpolation
• Operator theory on noncommutative varieties, II
• Some automorphism invariance properties for multicontractions
• Multivariable Bohr inequalities
• Unitary invariants in multivariable operator theory
• Invariant Subspaces and Hyper-Reflexivity for Free Semigroup Algebras
• Von Neumann inequality for $(B(\mathscr{H})^n)_1$.
• Standard Models for some Commuting Multioperators
• A Generalization of Von Neumann's Inequality to the Complex Ball
• Bohr’s power series theorem in several variables
• Similarity and ergodic theory of positive linear maps
• Standard noncommuting and commuting dilations of commuting tuples
• A non-commutative Positivstellensatz on isometries
• The curvature invariant of a Hilbert module over ℂ [z1, ..., zd]
• A positivstellensatz for non-commutative polynomials
• Standard operator models in the polydisc, II
• Non-commutative disc algebras and their representations
• Multidimensional analogues of Bohr’s theorem on power series
• Operator theory on noncommutative varieties
• Generalized Interpolation in H ∞
• Lax-Phillips scattering and conservative linear systems: a Cuntz-algebra multidimensional setting
• Eine Spektraltheorie für allgemeine Operatoren eines unitären Raumes. Erhard Schmidt zum 75. Geburtstag in Verehrung gewidmet
• Positive Functions on C ∗ -Algebras
• Structure and entropy for positive-definite Toeplitz kernels on free semigroups
• Similarity problems and completely bounded maps. Includes the solution to ``The Halmos problem.
• Curvature invariant for Hilbert modules over free semigroup algebras
• The curvature invariant of a non-commuting \(n\)-tuple

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