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Commutants and complex symmetry of finite Blaschke product multiplication operator in $L^2(\mathbb{T})$.

Authors :
Chattopadhyay, Arup
Das, Soma
Source :
Proceedings of the Edinburgh Mathematical Society; Feb2024, Vol. 67 Issue 1, p261-286, 26p
Publication Year :
2024

Abstract

Consider the multiplication operator M<subscript>B</subscript> in $L^2(\mathbb{T})$ , where the symbol B is a finite Blaschke product. In this article, we characterize the commutant of M<subscript>B</subscript> in $L^2(\mathbb{T})$. As an application of this characterization result, we explicitly determine the class of conjugations commuting with $M_{z^2}$ or making $M_{z^2}$ complex symmetric by introducing a new class of conjugations in $L^2(\mathbb{T})$. Moreover, we analyse their properties while keeping the whole Hardy space, model space and Beurling-type subspaces invariant. Furthermore, we extended our study concerning conjugations in the case of finite Blaschke products. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
00130915
Volume :
67
Issue :
1
Database :
Complementary Index
Journal :
Proceedings of the Edinburgh Mathematical Society
Publication Type :
Academic Journal
Accession number :
175724402
Full Text :
https://doi.org/10.1017/S0013091523000809