Perturbation theory for groups and lattices
type: Item
instance of: scholarly article
title: Perturbation theory for groups and lattices
zbMATH Open document ID: 0543.47030
DOI: 10.1016/0022-1236(83)90045-9
author: William Arveson
published in: Journal of Functional Analysis
publication date: 1983-01-01T00:00:00Z
review text: This paper contains a generalization of a theorem of Voiculescu which shows that, under separability assumptions, certain perturbed (by compacts) \(C^*\)-algebras of operators are unitarily equivalent. It is shown that this conclusion may fail in the inseparable case. The author gives reasons for seeking a generalization to certain inseparable \(C^*\)-algebras and, among other results, obtains such a generalization. This is applied to solve a problem relating to the perturbation theory of unitary group representations and to a problem of commutative subspace lattices, which extends a theorem of Anderson on compact perturbations of nests.
Mathematics Subject Classification ID: 47C15
Mathematics Subject Classification ID: 47A55
Mathematics Subject Classification ID: 22D10
Mathematics Subject Classification ID: 47L30
zbMATH DE Number: 3863919
zbMATH Keywords: inseparable \(C^*\)-algebras
zbMATH Keywords: perturbation theory of unitary group representations
zbMATH Keywords: commutative subspace lattices
zbMATH Keywords: compact perturbations of nests
MaRDI profile type: Publication
full work available at URL: 0022-1236(83)90045-9
OpenAlex ID: W2085756357
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description: scientific article; zbMATH DE number 3863919