2024-02-29T00:50:15Zhttps://docta.ucm.es/rest/oai/requestoai:docta.ucm.es:20.500.14352/717182023-08-05T23:44:04Zcom_20.500.14352_14col_20.500.14352_15
Gallardo-Gutiérrez, Eva A.
Partington, Johathan R.
2023-06-22T10:48:58Z
2023-06-22T10:48:58Z
2022
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0022-247X
https://hdl.handle.net/20.500.14352/71718
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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Multiplication by a finite Blaschke product on weighted Bergman spaces: Commutant and reducing subspaces
journal article