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 Blachke products B acting on weighted Bergman spaces which, as a particular instance, yields the case B(z) = z n on the Bergman space solved recently by by Abkar, Cao and Zhu [2]. Moreover, it extends...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2022 |
| País: | España |
| Institución: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/71718 |
| Acceso en línea: | https://hdl.handle.net/20.500.14352/71718 |
| Access Level: | acceso abierto |
| Palabra clave: | 517.553 Finite Blaschke products Commutants Reducing subspaces Bergman spaces Matemáticas (Matemáticas) Análisis matemático 12 Matemáticas 1202 Análisis y Análisis Funcional |
| Sumario: | We provide a characterization of the commutant of analytic Toeplitz operators TB induced by finite Blachke products B acting on weighted Bergman spaces which, as a particular instance, yields the case B(z) = z n on the Bergman space solved recently by by Abkar, Cao and Zhu [2]. 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 reducing subspaces of TB in the classical Bergman space. As a particular instance, we provide a direct proof of a theorem of Hu, Sun, Xu and Yu [18] which states that every analytic Toeplitz operator TB induced by a finite Blachke product on the Bergman space is reducible and the restriction of TB on a reducing subspace is unitarily equivalent to the Bergman shift. |
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