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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Published in | Journal of mathematical analysis and applications Vol. 515; no. 1; p. 126383 |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
Elsevier Inc
01.11.2022
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Subjects | |
Online Access | Get full text |
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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. |
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ISSN: | 0022-247X 1096-0813 |
DOI: | 10.1016/j.jmaa.2022.126383 |