International Journal of Mathematics and Mathematical Sciences
Volume 2007 (2007), Article ID 92070, 21 pages
doi:10.1155/2007/92070

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 ℂN(N≥1) and let B(E) be the Banach algebra of all bounded linear operators on a Banach space E. Let HVb(G,E) and HV0(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 HVb(G,E) and HV0(G,E).