Topological structure in the space of (weighted) composition operators on weighted Banach spaces of holomorphic functions

We consider the topological structure problem for the space of composition operators as well as the space of weighted composition operators on weighted Banach spaces with sup-norm. For the first space, we prove that the set of all composition operators that differ from the given one by a compact ope...

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Main Authors:	Abanin, Alexander V., Khoi, Le Hai, Tien, Pham Trong
Other Authors:	School of Physical and Mathematical Sciences
Format:	Article
Language:	English
Published:	2021
Subjects:	Science::Mathematics Topological Structure Composition Operator
Online Access:	https://hdl.handle.net/10356/150814
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Institution:	Nanyang Technological University
Language:	English

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spelling	sg-ntu-dr.10356-1508142023-02-28T19:55:50Z Topological structure in the space of (weighted) composition operators on weighted Banach spaces of holomorphic functions Abanin, Alexander V. Khoi, Le Hai Tien, Pham Trong School of Physical and Mathematical Sciences Science::Mathematics Topological Structure Composition Operator We consider the topological structure problem for the space of composition operators as well as the space of weighted composition operators on weighted Banach spaces with sup-norm. For the first space, we prove that the set of all composition operators that differ from the given one by a compact operator is path connected; however, in general, it is not always a component. Furthermore, we show that the set of compact weighted composition operators is path connected, but it is not a component in the second space. Ministry of Education (MOE) Accepted version The authors would like to thank the referees for useful remarks and comments that led to the improvement of the paper. The main part of this article has been done during Pham Trong Tien’s stay at Vietnam Institute for Advanced Study in Mathematics (VIASM). He would like to thank the institution for hospitality and support. 2021-05-31T01:37:44Z 2021-05-31T01:37:44Z 2019 Journal Article Abanin, A. V., Khoi, L. H. & Tien, P. T. (2019). Topological structure in the space of (weighted) composition operators on weighted Banach spaces of holomorphic functions. Bulletin Des Sciences Mathematiques, 158, 102806-. https://dx.doi.org/10.1016/j.bulsci.2019.102806 0007-4497 0000-0002-4282-3449 https://hdl.handle.net/10356/150814 10.1016/j.bulsci.2019.102806 2-s2.0-85074133713 158 102806 en M4011724.110 (RG128/16) Bulletin des Sciences Mathematiques © 2019 Elsevier Masson SAS. All rights reserved. This paper was published in Bulletin des Sciences Mathematiques and is made available with permission of Elsevier Masson SAS. application/pdf
institution	Nanyang Technological University
building	NTU Library
continent	Asia
country	Singapore Singapore
content_provider	NTU Library
collection	DR-NTU
language	English
topic	Science::Mathematics Topological Structure Composition Operator
spellingShingle	Science::Mathematics Topological Structure Composition Operator Abanin, Alexander V. Khoi, Le Hai Tien, Pham Trong Topological structure in the space of (weighted) composition operators on weighted Banach spaces of holomorphic functions
description	We consider the topological structure problem for the space of composition operators as well as the space of weighted composition operators on weighted Banach spaces with sup-norm. For the first space, we prove that the set of all composition operators that differ from the given one by a compact operator is path connected; however, in general, it is not always a component. Furthermore, we show that the set of compact weighted composition operators is path connected, but it is not a component in the second space.
author2	School of Physical and Mathematical Sciences
author_facet	School of Physical and Mathematical Sciences Abanin, Alexander V. Khoi, Le Hai Tien, Pham Trong
format	Article
author	Abanin, Alexander V. Khoi, Le Hai Tien, Pham Trong
author_sort	Abanin, Alexander V.
title	Topological structure in the space of (weighted) composition operators on weighted Banach spaces of holomorphic functions
title_short	Topological structure in the space of (weighted) composition operators on weighted Banach spaces of holomorphic functions
title_full	Topological structure in the space of (weighted) composition operators on weighted Banach spaces of holomorphic functions
title_fullStr	Topological structure in the space of (weighted) composition operators on weighted Banach spaces of holomorphic functions
title_full_unstemmed	Topological structure in the space of (weighted) composition operators on weighted Banach spaces of holomorphic functions
title_sort	topological structure in the space of (weighted) composition operators on weighted banach spaces of holomorphic functions
publishDate	2021
url	https://hdl.handle.net/10356/150814
_version_	1759858244249976832

Topological structure in the space of (weighted) composition operators on weighted Banach spaces of holomorphic functions

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