Multiplication by a finite Blaschke product on weighted Bergman spaces: commutant and reducing subspaces

2021/05/17 by Gallardo-Gutiérrez, Eva A., Partington, Jonathan R.
#47A15 #47A55 #47B15 #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2105.07760

Abstract

We provide a characterization of the commutant of analytic Toeplitz operators T_B induced by finite Blachke 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 by Abkar, Cao and Zhu. 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 H^p for 1

Related

• Reducing subspaces for analytic multipliers of the Bergman space
• Multiplication operators on the Bergman space via analytic continuation
• Commutants of Analytic Toeplitz Operators on the Bergman Space
• Commutants of a certain class of Toeplitz operators
• Reducing subspaces of multiplication operators on the Dirichlet space