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Essential Norm and Weak Compactness of Composition Operators on Weighted Banach Spaces of Analytic Functions

Published:1999-06-01
Printed: Jun 1999
• José Bonet
• Paweł Domański
• Mikael Lindström
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Abstract

Every weakly compact composition operator between weighted Banach spaces $H_v^{\infty}$ of analytic functions with weighted sup-norms is compact. Lower and upper estimates of the essential norm of continuous composition operators are obtained. The norms of the point evaluation functionals on the Banach space $H_v^{\infty}$ are also estimated, thus permitting to get new characterizations of compact composition operators between these spaces.
 Keywords: weighted Banach spaces of holomorphic functions, composition operator, compact operator, weakly compact operator
 MSC Classifications: 47B38 - Operators on function spaces (general) 30D55 - ${H}^p$-classes46E15 - Banach spaces of continuous, differentiable or analytic functions

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