Abstract
Let X be a reflexive Banach space of functions analytic on a bounded plane domain G such that for every λ in G the
functional of evaluation at λ is bounded. Assume further that X contains the constants and admits multi-plication by the
independent variable z, Mz, as a bounded operator. We give sufficient conditions for Mz to be reflexive on X. Also, we
discuss a class of shifts that are reflexive, and powers of the operator Mz of multiplication by z on Weighted Hardy spaces
are shown to be reflexive. Also, we derive some spectral properties of a multiplication operator acting on invariant
subspaces for the multiplication operator Mz.
Keywords:
Banach spaces of analytic functions, multiplication operators, reflexive operator, multipliers, Caratheodory
hull, bounded point evaluation, weighted Hardy spaces, polynomially bounded, Invariant subspace.