Multiplication operators on weighted locally convex spaces of vector-valued analytic functions
Let \(V\) be an arbitary system of weights on an open connected subset \(G\) of \(\mathbb{C}^{n}(n \geq 1)\) and let \(H(G,E)\) be the space of all vector-valued analytic functions from \(G\) into the Banach space \(E\). Let \[ HV_{b}(G,E)=\{f \in H(G,E): vf(G) \quad\text{ is bounded in }E \quad \forall v \in V \} \] and \[ HV_{0}(G,E)=\{f \in H(G,E): vf \text{ vanishes at }\infty \text{ on }G \quad\forall v \in V \}. \] The paper consists of \(5\) Sections. In Section \(3\), the author gives characterizations of multiplication operators on the spaces \(HV_{b}(g,E)\) and \(HV_{0}(G,E)\) for different systems of weights \(V\) on \(G\). In Section \(4\), he characterizes operator-valued analytic mappings which generate invertible multiplication operators on the spaces \(HV_{b}(G,E)\) and \(HV_{0}(G,E)\). In Section \(5\), he deals with a \(C_{0}\)-group of multiplication operators together with a linear dynamical system.
scientific article; zbMATH DE number 2101758