Weighted composition operators on weighted locally convex spaces of analytic functions
type: Item
instance of: scholarly article
title: Weighted composition operators on weighted locally convex spaces of analytic functions
zbMATH Open document ID: 1088.47013
published in: Southeast Asian Bulletin of Mathematics
publication date: 2005-05-06T00:00:00Z
review text: Let \(V\) be an arbitrary system of weights on an open connected subset \(G\) of \(\mathbb{C}^N\) \((N>1)\). The weighted locally convex spaces of analytic functions, \(HV_b(G)\) and \(HV_0(G)\), with topology generated by seminorms which are weighted analogues of the supremum norm, are defined as \[ HV_b(G)=\{f\in H(G): vf \text{ is bounded on } G \text{ for each }v\in V\} \] and \[ HV_0(G)=\{f\in H(G): vf \text{ vanishes at infinity on }G\text{ for every }v\in V\}. \] The weighted composition operators induced by the analytic mappings \(\phi: G\rightarrow G\) and \(\pi: G\rightarrow \mathbb{C}\) and the invertible weighted composition operators on the spaces \(HV_b(G)\) and \(HV_0(G)\) for different systems of weights \(V\) on \(G\) are characterized in the present paper. Some examples are given to illustrate these theorems.
Mathematics Subject Classification ID: 47B33
Mathematics Subject Classification ID: 46E10
Mathematics Subject Classification ID: 47B37
Mathematics Subject Classification ID: 47B38
Mathematics Subject Classification ID: 30H05
zbMATH DE Number: 2166106
zbMATH Keywords: weighted locally convex space
zbMATH Keywords: weighted composition operator
zbMATH Keywords: system of weights
zbMATH Keywords: seminorm
author: J. S. Manhas
reviewed by: Pengyan Hu
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2166106