Reflexivity on Banach Spaces of Analytic Functions
Abstract
Let X be a Banach space of functions analytic on
a 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 admits multiplication by the independent variable
z, Mz, as a bounded operator. We give su±cient conditions for
Mz to be reflexive.
a 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 admits multiplication by the independent variable
z, Mz, as a bounded operator. We give su±cient conditions for
Mz to be reflexive.
Keywords
Banach spaces of analytic functions,
multiplication operators, reflexive operator, multipliers, Caratheodory
hull, bounded point evaluation.
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