2026-06-29T07:25:10Zhttps://docta.ucm.es/rest/oai/request

oai:docta.ucm.es:20.500.14352/717182023-08-05T21:44:04Zcom_20.500.14352_14col_20.500.14352_15

Multiplication by a finite Blaschke product on weighted Bergman spaces: Commutant and reducing subspaces Gallardo-Gutiérrez, Eva A. Partington, Johathan R. 517.553 Finite Blaschke products Commutants Reducing subspaces Bergman spaces Matemáticas (Matemáticas) Análisis matemático 12 Matemáticas 1202 Análisis y Análisis Funcional 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. Plan Nacional I+D Programa para Centros de Excelencia en Investigación y Desarrollo Severo Ochoa Ayuda extraordinaria a Centros de Excelencia Severo Ochoa Depto. de Análisis Matemático y Matemática Aplicada Fac. de Ciencias Matemáticas FALSE pub 2023-06-22T10:48:58Z 2023-06-22T10:48:58Z 2022 journal article https://hdl.handle.net/20.500.14352/71718 0022-247X eng PID2019-105979GB-I00 CEX2019-000904-S 20205CEX001 open access application/pdf Elsevier