Affiliation:
1. Department of Mathematics, Shiraz University, Iran
Abstract
Let𝒳be reflexive Banach space of functions analytic plane domainΩsuch that for everyλinΩthe functional of evaluation atλis bounded. Assume further that𝒳contains the constants andMzmultiplication by the independent variablez, is bounded operator on𝒳. We give sufficient conditions forMzto be reflexive. In particular, we prove that the operatorsMzonEP(Ω)and certainHaP(β)reflexive. We also prove that the algebra of multiplication operators on Bergman spaces is reflexive, giving simpler proof of result of Eschmeier.
Subject
Mathematics (miscellaneous)
Cited by
4 articles.
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1. Spatial Numerical Range of Operators on Weighted Hardy Spaces;International Journal of Mathematics and Mathematical Sciences;2011
2. Bounded analytic structure of the banach space of formal power series;Rendiconti del Circolo Matematico di Palermo;2002-10
3. Interpolating sequence on certain Banach spaces of analytic functions;Bulletin of the Australian Mathematical Society;2002-04
4. On the spacel P(β);Rendiconti del Circolo Matematico di Palermo;2000-02