Operator norms and essential norms of weighted composition operators between Banach spaces of analytic functions
type: Item
instance of: scholarly article
title: Operator norms and essential norms of weighted composition operators between Banach spaces of analytic functions
zbMATH Open document ID: 1338.30049
author: Flavia Colonna
author: Maria Tjani
published in: Journal of Mathematical Analysis and Applications
publication date: 2015-11-10T00:00:00Z
review text: Let \(\mu\) be a weight, that is, a positive continuous function on the unit disk \(\mathbb{D}\). The authors characterize the bounded weighted composition operators \(W_{\psi, \varphi}\) from a general Banach space of analytic functions \(X\) into the growth space \(H^\infty_\mu\) and present an exact formula for the operator norm. Under certain assumptions on \(X\), they characterize the corresponding compact operators and estimate the essential norm of \(W_{\psi, \varphi}\) when \(X\) is a reflexive Banach space. Such results are applied to the Hardy spaces, the weighted Bergman spaces, and the Bloch space. Also, the authors obtain analogous results for the operators \(W_{\psi, \varphi}\) from \(X\) into the Bloch-type space \(B_\mu\). Reviewer's remark. A similar axiomatic approach was earlier used by the reviewer [J. Math. Sci., New York 182, No. 5, 630--638 (2012); translation from Zap. Nauchn. Semin. POMI 389, 85--100 (2011; Zbl 1257.30065)] to characterize the bounded operators \(W_{\psi, \varphi}\) from \(X\) into the Lipschitz-type spaces of arbitrary smoothness.
reviewed by: Evgueni Doubtsov
Mathematics Subject Classification ID: 30H10
Mathematics Subject Classification ID: 30H20
Mathematics Subject Classification ID: 30H30
Mathematics Subject Classification ID: 47B33
zbMATH DE Number: 6506791
zbMATH Keywords: Hardy spaces
zbMATH Keywords: weighted Bergman spaces
zbMATH Keywords: Bloch spaces
zbMATH Keywords: composition operators
MaRDI profile type: Publication
full work available at URL: j.jmaa.2015.08.073
OpenAlex ID: W1234961072
cites work: An Integral Operator on Hp
cites work: Integration operators on Bergman spaces
cites work: Isometric weighted composition operators on weighted Banach spaces of type $H^\infty }$
cites work: Norm-attaining weighted composition operators on weighted Banach spaces of analytic functions
cites work: Weighted composition operators from Hardy spaces into logarithmic Bloch spaces
cites work: Weighted composition operators from the Besov spaces into the weighted-type space \(H_{\mu}^{\infty}\)
cites work: Essential norms of weighted composition operators from reproducing kernel Hilbert spaces into weighted-type spaces
cites work: Q4515420
cites work: Q3223360
cites work: Q4888816
cites work: On the exact norm value of some BMOA functions
cites work: Integral Means and Bmoa-Norms of Logarithms of Univalent Functions
cites work: Q4490700
cites work: The essential norm of weighted composition operators on weighted Banach spaces of analytic functions
cites work: Estimates of essential norms of weighted composition operators between Bloch-type spaces
cites work: Essential norms of weighted composition operators between Bloch-type spaces
cites work: Weighted Composition Operators on Weighted Banach Spaces of Analytic Functions
cites work: Q3016202
cites work: Q5703505
cites work: Q5484161
cites work: Q3070312
cites work: Essential norms of weighted composition operators from the \(\alpha \)-Bloch space to a weighted-type space on the unit ball
cites work: Q3011736
cites work: Compact composition operators on Besov spaces
cites work: A Sharp Estimate for A p α Functions in C n
cites work: Q3447431
cites work: Bloch type spaces of analytic functions
DOI: 10.1016/J.JMAA.2015.08.073
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description: scientific article; zbMATH DE number 6506791