Topological structure of the set of weighted composition operators on weighted Bergman spaces of infinite order

José Bonet; Mikael Lindström; Elke Wolf

doi:10.1007/s00020-009-1706-x

Topological structure of the set of weighted composition operators on weighted Bergman spaces of infinite order

José Bonet^*, Mikael Lindström, Elke Wolf

^*Corresponding author for this work

Mathematics

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

7 Citations (Scopus)

Abstract

We consider the topological space of all weighted composition operators on weighted Bergman spaces of infinite order endowed with the operator norm. We show that the set of compact weighted composition operators is path connected. Furthermore, we find conditions to ensure that two weighted composition operators are in the same path connected component if the difference of them is compact. Moreover, we compare the topologies induced by L(H^∞) and L(H^∞_ν) on the space of bounded composition operators and give a sufficient condition for a composition operator to be isolated.

Original language	English
Pages (from-to)	195-210
Number of pages	16
Journal	Integral Equations and Operator Theory
Volume	65
Issue number	2
DOIs	https://doi.org/10.1007/s00020-009-1706-x
Publication status	Published - Oct 2009
MoE publication type	A1 Journal article-refereed

Keywords

Topological structure
Weighted Bergman space of infinite order
Weighted composition operator

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10.1007/s00020-009-1706-x

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abstract = "We consider the topological space of all weighted composition operators on weighted Bergman spaces of infinite order endowed with the operator norm. We show that the set of compact weighted composition operators is path connected. Furthermore, we find conditions to ensure that two weighted composition operators are in the same path connected component if the difference of them is compact. Moreover, we compare the topologies induced by L(H∞) and L(H∞ν) on the space of bounded composition operators and give a sufficient condition for a composition operator to be isolated.",

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author = "Jos{\'e} Bonet and Mikael Lindstr{\"o}m and Elke Wolf",

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T1 - Topological structure of the set of weighted composition operators on weighted Bergman spaces of infinite order

AU - Bonet, José

AU - Lindström, Mikael

AU - Wolf, Elke

N1 - Funding Information: The research of José Bonet was partially supported by FEDER and MEC Project MTM 2007-62643 and Generalitat Valenciana project Prometeo/2008/101. Part of the present work was done during a stay of J. Bonet at the University of Paderborn in August 2008. The support of the Alexander von Humboldt Foundation is greatly appreciated.

PY - 2009/10

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N2 - We consider the topological space of all weighted composition operators on weighted Bergman spaces of infinite order endowed with the operator norm. We show that the set of compact weighted composition operators is path connected. Furthermore, we find conditions to ensure that two weighted composition operators are in the same path connected component if the difference of them is compact. Moreover, we compare the topologies induced by L(H∞) and L(H∞ν) on the space of bounded composition operators and give a sufficient condition for a composition operator to be isolated.

AB - We consider the topological space of all weighted composition operators on weighted Bergman spaces of infinite order endowed with the operator norm. We show that the set of compact weighted composition operators is path connected. Furthermore, we find conditions to ensure that two weighted composition operators are in the same path connected component if the difference of them is compact. Moreover, we compare the topologies induced by L(H∞) and L(H∞ν) on the space of bounded composition operators and give a sufficient condition for a composition operator to be isolated.

KW - Topological structure

KW - Weighted Bergman space of infinite order

KW - Weighted composition operator

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DO - 10.1007/s00020-009-1706-x

M3 - Article

AN - SCOPUS:71549127718

SN - 0378-620X

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EP - 210

JO - Integral Equations and Operator Theory

JF - Integral Equations and Operator Theory

IS - 2

ER -

Topological structure of the set of weighted composition operators on weighted Bergman spaces of infinite order

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Keywords

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