Composition Operators and Multiplication Operators on Weighted Spaces of Analytic Functions

Abstract

LetVbe an arbitrary system of weights on an open connected subsetGofℂN(N≥1)and letB(E)be the Banach algebra of all bounded linear operators on a Banach spaceE. LetHVb(G,E)andHV0(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 functionsH(G)to the weighted spaces of analytic functionsHVb(G,E)andHV0(G,E).