Topological structure of the space of composition operators on the Hardy space of Dirichlet series

The aim of this paper is to study when two composition operators on the Hilbert space of Dirichlet series with square summable coefficients belong to the same component or when their difference is compact. As a corollary we show that if a linear combination of composition operators with polynomial s...

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Bibliographic Details
Published in:Journal of functional analysis Vol. 289; no. 11; p. 111134
Main Authors: Bayart, Frédéric, Wang, Maofa, Yao, Xingxing
Format: Journal Article
Language:English
Published: Elsevier Inc 01.12.2025
Elsevier
Subjects:
Composition operator
Dirichlet series
Functional Analysis
Linear combination
Mathematics
Topological structure
secondary
Topological structure
Dirichlet series
Linear combination
Composition operator
primary
2010 Mathematics Subject Classification. Primary 47B33
topological structure
Secondary 30B50
linear combination
compactness
46E15 Composition operator
ISSN:0022-1236, 1096-0783
Online Access:Get full text
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Summary:The aim of this paper is to study when two composition operators on the Hilbert space of Dirichlet series with square summable coefficients belong to the same component or when their difference is compact. As a corollary we show that if a linear combination of composition operators with polynomial symbols of degree at most 2 is compact, then each composition operator is compact.
ISSN:0022-1236
1096-0783
DOI:10.1016/j.jfa.2025.111134