Topological centers of module actions induced by unitary representations
type: Item
instance of: scholarly article
title: Topological centers of module actions induced by unitary representations
zbMATH Open document ID: 1214.46030
author: Pak-Keung Chan
published in: Journal of Functional Analysis
publication date: 2010-10-18T00:00:00Z
review text: Let \(G\) be a locally compact group. Let \(LUC(G)\) denote the Banach space of all left uniformly continuous functions on \(G\). Then the dual space \(LUC(G)^*\) becomes a Banach algebra. Let \(\pi\) be a unitary representation of \(G\) on a complex Hilbert space \(H\). Then \(UCB(\pi)\) denotes the unital \(C^*\)-algebra of \(B(H)\) consisting of the operators \(T\in B(H)\) such that the map \(t\mapsto\pi(t^{-1})T\pi(t)\) is continuous. The Banach space \(UCB(\pi)^*\) becomes a Banach left \(LUC(G)^*\)-module in a natural way. The author studies the topological center of this module. A characterisation of when the center is minimal and also conditions for the center to be maximal are given. Various examples whose topologial centers are maximal, minimal or neither are also given.
Mathematics Subject Classification ID: 46H25
Mathematics Subject Classification ID: 22D10
Mathematics Subject Classification ID: 43A20
zbMATH DE Number: 5801188
zbMATH Keywords: Arens product
zbMATH Keywords: bounded bilinear map
zbMATH Keywords: Banach G-module
zbMATH Keywords: unitary representation
zbMATH Keywords: topological center
zbMATH Keywords: module action
reviewed by: Armando R. Villena
MaRDI profile type: Publication
full work available at URL: j.jfa.2010.06.006
OpenAlex ID: W1986481264
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DOI: 10.1016/J.JFA.2010.06.006
description: scientific article; zbMATH DE number 5801188