Multiplication by a finite Blaschke product on weighted Bergman spaces: Commutant and reducing subspaces

We provide a characterization of the commutant of analytic Toeplitz operators TB induced by finite Blaschke products B acting on weighted Bergman spaces which, as a particular instance, yields the case B(z)=zn on the Bergman space solved recently by Abkar, Cao and Zhu [1]. Moreover, it extends previ...

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Bibliographic Details
Published inJournal of mathematical analysis and applications Vol. 515; no. 1; p. 126383
Main Authors Gallardo-Gutiérrez, Eva A., Partington, Jonathan R.
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.11.2022
Subjects
Bergman spaces
Commutants
Finite Blaschke products
Reducing subspaces
Reducing subspaces
Bergman spaces
Finite Blaschke products
Commutants
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Summary:We provide a characterization of the commutant of analytic Toeplitz operators TB induced by finite Blaschke products B acting on weighted Bergman spaces which, as a particular instance, yields the case B(z)=zn on the Bergman space solved recently by Abkar, Cao and Zhu [1]. Moreover, it extends previous results by Cowen and Wahl in this context and applies to other Banach spaces of analytic functions such as Hardy spaces Hp for 1<p<∞. Finally, we apply this approach to study the reducing subspaces of TB in weighted Bergman spaces.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2022.126383