Operators acting on certain Banach spaces of analytic functions

Abstract

Let 𝒳 be reflexive Banach space of functions analytic plane domain Ω such that for every λ in Ω the functional of evaluation at λ is bounded. Assume further that 𝒳 contains the constants and Mz multiplication by the independent variable z, is bounded operator on 𝒳. We give sufficient conditions for Mz to be reflexive. In particular, we prove that the operators Mz on EP(Ω) and certain HaP(β) reflexive. We also prove that the algebra of multiplication operators on Bergman spaces is reflexive, giving simpler proof of result of Eschmeier.

Keywords

• Banach spaces of analytic functions
• Smirnov domain
• bounded point evaluation.