Isolated points and essential components of composition operators on 𝐻^{∞}

DOI10.1090/S0002-9939-01-06233-5zbMath1008.47031MaRDI QIDQ2781347

Takuya Hosokawa, Kei-Ji Izuchi, DeChao Zheng

Publication date: 19 March 2002

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

zbMATH Keywords

composition operatorscompact operatorsisolationbounded analytic functionsasymptotically interpolating sequences

Mathematics Subject Classification ID

Linear operators on function spaces (general) (47B38) Linear composition operators (47B33)

Related Items (37)

Topological structure of the space of composition operators on \(\mathcal{H}^\infty\) of Dirichlet series ⋮ WEAKLY COMPACT DIFFERENCES OF (WEIGHTED) COMPOSITION OPERATORS ⋮ Essential norm of differences of weighted composition operators between weighted-type spaces on the unit ball ⋮ Differences of composition operators on weighted Banach spaces of holomorphic functions defined on the unit ball of a complex Banach space ⋮ Compact differences of weighted composition operators from weighted Bergman spaces to weighted-type spaces ⋮ Thin sequences and their role in \(H^p\) theory, model spaces, and uniform algebras ⋮ Norm-attaining weighted composition operators on weighted Banach spaces of analytic functions ⋮ Topological structure of the space of composition operators on \(L^{\infty}\) of an unbounded, locally finite metric space ⋮ DIFFERENCES OF COMPOSITION OPERATORS BETWEEN WEIGHTED BANACH SPACES OF HOLOMORPHIC FUNCTIONS ⋮ Components of linear fractional composition operators on spaces of holomorphic functions ⋮ Difference of generalized integration operators on the space of Cauchy transforms ⋮ Weighted composition operators on the space of bounded harmonic functions ⋮ Compact differences of composition operators on Bloch and Lipschitz spaces ⋮ Hilbert-Schmidt differences of composition operators on the Bergman space ⋮ Path Connected Components in the Spaces of Weighted Composition Operators with the Strong Operator Topology II ⋮ Extreme points of the closed convex hull of composition operators ⋮ Topological properties of path connected components in spaces of weighted composition operators into \(L^{1}\) ⋮ Norms and essential norms of linear combinations of endomorphisms ⋮ Linear combinations of composition operators on \(H^{\infty }\) ⋮ Difference of weighted composition operators ⋮ Essential norm of the difference of weighted composition operators ⋮ Differences of weighted composition operations on the unit polydisk ⋮ Linear sums of two composition operators on the Fock space ⋮ Sums of weighted composition operators on \(H^\infty\) ⋮ Topological structure in the space of (weighted) composition operators on weighted Banach spaces of holomorphic functions ⋮ Thin sequences and their role in model spaces and Douglas algebras ⋮ Topological components of the space of composition operators on Fock spaces ⋮ Differences of composition operators on the space of bounded analytic functions in the polydisc ⋮ Spectra of weighted composition operators on analytic function spaces ⋮ Homomorphisms between algebras of holomorphic functions on the infinite polydisk ⋮ Differences of weighted composition operators acting from Bloch space to 𝐻^{∞} ⋮ Composition operators and Gleason's problem on weighted Fock spaces ⋮ Linear combinations of composition operators on \(H^{\infty }\) spaces over the unit ball and polydisk ⋮ Path connected components in weighted composition operators on $h^\infty $ and $H^\infty $ with the operator norm ⋮ Differences of composition operators between weighted-type spaces of holomorphic functions on the unit ball of \(\mathbb C^N\) ⋮ Composition operators on uniform algebras, essential norms, and hyperbolically bounded sets ⋮ Topological structures of the sets of composition operators on the Bloch spaces

Cites Work

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• Extreme points and extremum problems in \(H_1\)
• Isolation amongst the composition operators
• Composition operators and classical function theory
• Components in the space of composition operators
• Decompositions of the Maximal Ideal Space of L ∞
• Topological structure of the space of composition operators on \(H^\infty\).

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