Invertible weighted composition operators on weighted function spaces
type: Item
instance of: scholarly article
title: Invertible weighted composition operators on weighted function spaces
zbMATH Open document ID: 0854.47019
DOI: 10.1007/BF01904058
author: R. K. Singh
author: J. S. Manhas
published in: Analysis Mathematica
publication date: 1995-02-13T00:00:00Z
review text: If \(X\) is a completely regular Hausdorff space and \(E\) a locally convex Hausdorff topological vector space, let \(C(X, E)\) denote the space of all continuous functions from \(X\) into \(E\). Also let \(L(X)\) be a topological vector subspace of the Cartesian product \(\prod_{x\in X} F_x\) where \((X, (F_x )_{x\in X})\) is a vector filtration over \(X\). For suitable systems \(V\) of weights on \(X\), the authors define weighted spaces of continuous functions \(CV_b (X, E)\) and \(CV_0 (X, E)\) (both are contained in \(C(X, E)\)), and weighted spaces of cross-sections over \(X\), \(LV_b (X)\), \(LV_0 (X)\) (both are contained in \(L(X)\)). These are locally convex spaces under suitable seminorms. For \(\varphi: X\to X\) and \(\pi: X\to E\) continuous mappings define the weighted composition operator \(W_{\pi, \varphi} (f)= \pi(f \circ \varphi)\). The authors characterize those \(W_{\pi, \varphi}\) that are invertible as operators on \(CV_0 (X, E)\) or on \(LV_0 (X)\).
Mathematics Subject Classification ID: 47B38
Mathematics Subject Classification ID: 46E40
Mathematics Subject Classification ID: 46E10
zbMATH DE Number: 721632
zbMATH Keywords: composition operators
zbMATH Keywords: completely regular Hausdorff space
zbMATH Keywords: locally convex Hausdorff topological vector space
zbMATH Keywords: vector filtration
zbMATH Keywords: weighted spaces of continuous functions
zbMATH Keywords: weighted spaces of cross-sections
reviewed by: Aristomenis G. Siskakis
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 721632