Operator Norms and Essential Norms of WeightedComposition Operators from Analytic Function Spaces into Zygmund-type Spaces

In this work, we characterize the bounded and compact weighted composition operators from a large class of Banach spaces X of analytic functions on the open unit disk into Zygmund-type spaces. Under more restrictive conditions, we provide an approximation of the essential norm of such operators. We...

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Published in:Complex analysis and operator theory 2020-01, Vol.14 (6)
Main Authors: Shams, Alyusof, Colonna Flavia
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Language:English
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Analytic functions
Banach spaces
Composition
Function space
Mathematical analysis
Mathematics
Norms
Operators (mathematics)
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description In this work, we characterize the bounded and compact weighted composition operators from a large class of Banach spaces X of analytic functions on the open unit disk into Zygmund-type spaces. Under more restrictive conditions, we provide an approximation of the essential norm of such operators. We also show that all bounded weighted composition operators from X to the little Zygmund-type space are compact and characterize such operators. We apply our results to the cases when X is the Hardy space Hp for 1≤p≤∞ and the weighted Bergman space Aαp for α>-1 and 1≤p
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subjects Analytic functions
Banach spaces
Composition
Function space
Mathematical analysis
Mathematics
Norms
Operators (mathematics)
title Operator Norms and Essential Norms of WeightedComposition Operators from Analytic Function Spaces into Zygmund-type Spaces
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