Essential norm and weak compactness of composition operators on weighted Banach spaces of analytic functions

José Bonet; Paweł Domański; Mikael Lindström

doi:10.4153/CMB-1999-016-x

Essential norm and weak compactness of composition operators on weighted Banach spaces of analytic functions

José Bonet
, Paweł Domański
, Mikael Lindström

Mathematics

Research output: Contribution to journal › Article › Scientific › peer-review

104 Citations (Scopus)

Abstract

Every weakly compact composition operator between weighted Banach spaces H^∞_v 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 are also estimated, thus permitting to get new characterizations of compact composition operators between these spaces.

Original language	English
Pages (from-to)	139-148
Number of pages	10
Journal	Canadian Mathematical Bulletin
Volume	42
Issue number	2
DOIs	https://doi.org/10.4153/CMB-1999-016-x
Publication status	Published - Jun 1999
MoE publication type	A1 Journal article-refereed

Keywords

Compact operator
Composition operator
Weakly compact operator
Weighted Banach spaces of holomorphic functions

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10.4153/CMB-1999-016-x

Cite this

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AU - Bonet, José

AU - Domański, Paweł

AU - Lindström, Mikael

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Y1 - 1999/6

N2 - Every weakly compact composition operator between weighted Banach spaces H∞v 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 are also estimated, thus permitting to get new characterizations of compact composition operators between these spaces.

AB - Every weakly compact composition operator between weighted Banach spaces H∞v 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 are also estimated, thus permitting to get new characterizations of compact composition operators between these spaces.

KW - Compact operator

KW - Composition operator

KW - Weakly compact operator

KW - Weighted Banach spaces of holomorphic functions

UR - https://www.scopus.com/pages/publications/0000410554

U2 - 10.4153/CMB-1999-016-x

DO - 10.4153/CMB-1999-016-x

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AN - SCOPUS:0000410554

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VL - 42

SP - 139

EP - 148

JO - Canadian Mathematical Bulletin

JF - Canadian Mathematical Bulletin

IS - 2

ER -

Essential norm and weak compactness of composition operators on weighted Banach spaces of analytic functions

Abstract

Keywords

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