An imprimitivity theorem for representations of locally compact groups on arbitrary Banach spaces
type: Item
instance of: scholarly article
title: An imprimitivity theorem for representations of locally compact groups on arbitrary Banach spaces
zbMATH Open document ID: 0893.22003
author: Niels Grønbæk
published in: Pacific Journal of Mathematics
publication date: 1997-09-16T00:00:00Z
review text: We prove a general version of Mackey's imprimitivity theorem for induced representations of locally compact groups. Let \(G\) be a locally compact group and let \(H\) be a closed subgroup. Following Rieffel we show, using Morita equivalence of Banach algebras, that systems of imprimitivity for induction from strongly continuous Banach \(H\)-modules to strongly continuous Banach \(G\)-modules can be described in terms of an action on the induced module of \(C_0(G/H)\), the algebra of complex continuous functions on \(G/H\) vanishing at \(\infty\), which is compatible with the \(G\)-homogeneous structure of \(G/H\) and the strong operator topology continuity of the module action of \(G\).
Mathematics Subject Classification ID: 22D12
Mathematics Subject Classification ID: 22D30
Mathematics Subject Classification ID: 16D90
Mathematics Subject Classification ID: 46H15
zbMATH DE Number: 1060832
zbMATH Keywords: Mackey's imprimitivity theorem
zbMATH Keywords: induced representations
zbMATH Keywords: locally compact groups
zbMATH Keywords: Banach algebras
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1060832