Commutants and Complex Symmetry of Finite Blaschke Product Multiplication Operator in \bmL²(\T)

2021/10/24 by Arup Chattopadhyay, Soma Das, Chattopadhyay, Arup +1
Mathematics · #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2110.12453

openalex publication_date 2021/10/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Consider the multiplication operator M_B in L²(\T), where the symbol B is a finite Blaschke product. In this article, we characterize the commutant of M_B in L²(\T), noting the fact that L²(\T) is not an RKHS. As an application of this characterization result, we explicitly determine the class of conjugations commuting with M_z² or making M_z² complex symmetric by introducing a new class of conjugations in L²(\T). Moreover, we analyze 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.

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