A note on Hilbert \(C^*\)-modules associated with a foliation
type: Item
instance of: scholarly article
title: A note on Hilbert \(C^*\)-modules associated with a foliation
zbMATH Open document ID: 0594.46048
author: Shigeru Yamagami
published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University
publication date: 1984-01-01T00:00:00Z
review text: Let (M,\({\mathfrak F})\) be a \(C^{\infty,0}\) \((C^{\infty}\) along leaves and \(C^ 0\) along transversal direction) foliation \(C^*\)-algebra with its holonomy group G Hausdorff. The author studies some properties of the Hilbert \(C^*\)-module \(E^{W_ 2}_{W_ 1}\) corresponding to two transversal submanifolds \(W_ 1\) and \(W_ 2\) of M and proves that \({\mathcal K}(E_ T^{W_ 1},E_ T^{W_ 2})\cong E^{W_ 2}_{W_ 1}\), where \({\mathcal K}(E_ T^{W_ 1},E_ T^{W_ 2})\) denotes the set of compact operators from \(E_ 1\) and \(E_ 2\). This reduces to a result of Hilsum and Skandali when \(W_ 1=W_ 2\).
Mathematics Subject Classification ID: 46H25
Mathematics Subject Classification ID: 46L05
Mathematics Subject Classification ID: 46M20
Mathematics Subject Classification ID: 57R30
zbMATH DE Number: 3955742
zbMATH Keywords: foliation \(C^*\)-algebra
zbMATH Keywords: holonomy group
zbMATH Keywords: Hilbert \(C^*\)-module
zbMATH Keywords: transversal submanifolds
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2977/prims/1195181830
OpenAlex ID: W2267347129
cites work: Q4200733
cites work: Q3319255
cites work: A groupoid approach to C*-algebras
cites work: Induced representations of C\(^*\)-algebras
DOI: 10.2977/PRIMS/1195181830
description: scientific article; zbMATH DE number 3955742