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International Journal of Mathematics and Mathematical Sciences
Volume 2007, Article ID 92070, 21 pages
http://dx.doi.org/10.1155/2007/92070
Research Article

Composition Operators and Multiplication Operators on Weighted Spaces of Analytic Functions

J. S. Manhas

Department of Mathematics and Statistics, College of Science, Sultan Qaboos University, P.O. Box 36, Muscat 123, Oman

Received 17 June 2006; Accepted 26 April 2007

Academic Editor: Marianna A. Shubov

Copyright © 2007 J. S. Manhas. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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).