RT Journal Article
T1 Multiplication by a finite Blaschke product on weighted Bergman spaces: Commutant and reducing subspaces
A1 Gallardo-Gutiérrez, Eva A.
A1 Partington, Johathan R.
AB 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.
PB Elsevier
SN 0022-247X
YR 2022
FD 2022
LK https://hdl.handle.net/20.500.14352/71718
UL https://hdl.handle.net/20.500.14352/71718
LA eng
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