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International Journal of Mathematics and Mathematical Sciences
Volume 18, Issue 1, Pages 107-110
http://dx.doi.org/10.1155/S0161171295000147

Operators acting on certain Banach spaces of analytic functions

Department of Mathematics, Shiraz University, Iran

Received 14 January 1993; Revised 21 September 1993

Copyright © 1995 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.