Composition Operators and Multiplication Operators on Weighted Spaces of Analytic Functions

Manhas, J. S.

doi:https://doi.org/10.1155/2007/92070

International Journal of Mathematics and Mathematical Sciences

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Research Article | Open Access

Volume 2007 | Article ID 092070 | https://doi.org/10.1155/2007/92070

Composition Operators and Multiplication Operators on Weighted Spaces of Analytic Functions

J. S. Manhas¹

Academic Editor: Marianna A. Shubov

Received17 Jun 2006

Accepted26 Apr 2007

Published23 Jan 2008

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).

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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.

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