J. S. Manhas

Multiplication Operators and Dynamical Systems on Weighted Locally Convex
Spaces of Holomorphic Functions

Let $G$ be an open subset of $\mathbb{C}$ and let $V$ be an arbitrary system of weights on $G.$ Let $HV_{b}(G)$ and $HV_{0}(G)$ be the weighted locally convex spaces of holomorphic functions with a topology generated by seminorms which are weighted analogues of the supremum norm. In the present article, we characterize the analytic functions inducing multiplication operators and invertible multiplication operators on the spaces $HV_{b}(G)$ and $HV_{0}(G)$ for different systems of weights $V$ on $G$. A (linear) dynamical system induced by multiplication operators on these spaces is obtained as an application of the theory of multiplication operators.

Weighted locally convex spaces of holomorphic functions, arbitrary system of weights, seminorms, multiplication operators, invertible multiplication operators, dynamical systems.

MSC 2000: Primary: 47B37, 47B38, 46E10; secondary: 47D03, 37B05, 32A10, 30H05.