Differences of composition operators between weighted banach spaces of holomorphic functions
TLDR
In this paper, the authors consider differences of composition operators between given weighted Banach spaces or Hv0 of analytic functions with weighted sup-norms and give estimates for the distance of these differences to the space of compact operators.Abstract:
We consider differences of composition operators between given weighted Banach spaces or Hv0 of analytic functions with weighted sup-norms and give estimates for the distance of these differences to the space of compact operators. We also study boundedness and compactness of the operators. Some examples illustrate our results.read more
Citations
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Essential norm of the difference of weighted composition operators
Mikael Lindström,Elke Wolf +1 more
TL;DR: In this article, the essential norm of differences of composition operators acting on Bloch-type spaces has been derived for analytic functions with weighted sup-norms, and the authors apply their result to estimate the fundamental norm of these differences.
Journal ArticleDOI
Weighted composition operators from weighted Bergman spaces to weighted-type spaces on the unit ball
TL;DR: The operator norm of the weighted composition operator is calculated from a weighted Bergman space to a weighted-type space on the unit ball of C^n and the compactness of the operator is characterized.
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Compact Differences of Composition Operators on Bloch and Lipschitz Spaces
TL;DR: In this article, the authors consider the difference T = Cφ − Cψ of two analytic composition operators in the unit disc and characterize the compactness and weak compactness of T on the standard Bloch space, improving an earlier result by Hosokawa and Ohno.
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An application of atomic decomposition in Bergman spaces to the study of differences of composition operators
TL;DR: In this paper, the authors characterize bounded differences of composition operators from standard weighted Bergman spaces A α p into Lebesgue spaces L q ( μ ) when α > − 1 and p > q.
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Differences of generalized composition operators on the Bloch space
TL;DR: The boundedness and compactness of the differences of two generalized composition operators on the Bloch space in the unit disk are investigated in this paper, where they are shown to be bounded and compact.
References
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Book
Bounded Analytic Functions
TL;DR: In this article, the Corona construction was used to construct Douglas algebra and interpolating sequences and Maximal Ideals were used to solve a set of problems in the Corona Construction.
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Composition Operators: and Classical Function Theory
TL;DR: The study of composition operators forges links between fundamental properties of linear operators and results from the classical theory of analytic functions as mentioned in this paper and provides a self-contained introduction to both the subject and its function-theoretic underpinnings.
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On bounded analytic functions
TL;DR: In this article, the authors give an alternative derivation of results on bounded analytic functions recently obtained by Ahlfors [1] and Garabedian [2] and show that the main idea to be used is more in the nature of a lucky guess than of a method.
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Banach Spaces for Analysts
TL;DR: In this paper, the authors present an introduction to modern Banach space theory, in which applications to other areas such as harmonic analysis function theory, orthogonal series and approximation theory are also given prominence.