HOMOMORPHISMS AND COMPOSITION OPERATORS ON WEIGHTED SPACES OF ANALYTIC FUNCTIONS

Abstract

Let be an arbitrary system of weights on an open connected subset of C. . Let and be the weighted locally convex spaces of analytic functions with a topology generated by seminorms which are weighted analogues of the supremum norm. In the present article, we characterize all continuous linear transformations on the spaces and which are composition operators. Also, for some system of weights, we have proved that homomorphisms on weighted algebras of analytic functions are composition operators.

2000 Mathematics Subject Classification: Primary 47B37, 47B38, 47B07, 46E10 Secondary 47D03, 37B05, 30H05.

Keywords and phrases: Weighted locally convex spaces of analytic functions, system of weights, seminorms, composition operators, homomorphisms.