Composition Operators and Multiplication Operators on Weighted Spaces of Analytic Functions

摘要

LetVbe an arbitrary system of weights on an open connected subsetGof?N(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-valuedanalytic functions. In this survey, we present a development of the theoryof multiplication operators and composition operators from classical spaces ofanalytic functionsH(G)to the weighted spaces of analytic functionsHVb(G,E)andHV0(G,E).