Compact multipliers
type: Item
instance of: scholarly article
title: Compact multipliers
zbMATH Open document ID: 0917.43001
author: Gilbert L. Muraz
published in: Bulletin of the Belgian Mathematical Society - Simon Stevin
publication date: 1999-04-05T00:00:00Z
full work available at URL: https://eudml.org/doc/119837
review text: Recall that a Banach \(G\)-module (resp. \(L^1(G)\)-module) is a Banach space \(E\) with an action \((x,e)\in G\times E\to L_xe\in E\) of a locally compact abelian group \(G\) (resp. \((f,e)\to T_fe\) of the convolution algebra \(L^1(G))\). In a Banach module one can define almost periodic elements as those giving rise, via the \(L^1(G)\)-action, to compact operators from \(L^1(G)\) into \(E\). An exhaustive study of Banach modules appeared in the joint work of the author with \textit{C. Datry} [Bull. Sci. Math. 119, 299-337 (1995; Zbl 0840.43005); ibid. 120, 493-536 (1996; Zbl 0871.43002)]. In the present paper multipliers from one Banach module into another (bounded linear operators which are \(L^1(G)\)-morphisms) are studied; these form a Banach module in its own right. It is shown that compact multipliers are almost periodic with the converse being valid under some natural conditions on the Banach modules in question. Some results about the approximation of compact multipliers by finite dimensional ones are also obtained.
Mathematics Subject Classification ID: 43A22
Mathematics Subject Classification ID: 43A60
zbMATH DE Number: 1266841
zbMATH Keywords: Banach \(G\)-module
zbMATH Keywords: locally compact abelian group
zbMATH Keywords: almost periodic elements
zbMATH Keywords: multipliers
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1266841