Composition Operators and Multiplication Operators on Weighted Spaces of Analytic Functions

Abstract

Let V be an arbitrary system of weights on an open connected subset G of ℂ N ( N ≥ 1 ) and let B ( E ) be the Banach algebra of all bounded linear operators on a Banach space E . Let H V b ( G , E ) and H V 0 ( G , E ) be the weighted locally convex spaces of vector-valued analytic functions. In this survey, we present a development of the theory of multiplication operators and composition operators from classical spaces of analytic functions H ( G ) to the weighted spaces of analytic functions H V b ( G , E ) and H V 0 ( G , E ) .