Translation group and spectrum condition
type: Item
instance of: scholarly article
title: Translation group and spectrum condition
zbMATH Open document ID: 0578.46060
DOI: 10.1007/BF01217346
published in: Communications in Mathematical Physics
publication date: 1984-01-01T00:00:00Z
review text: Let A be a \(C^*\)-algebra on which \({\mathbb{R}}^ d\) acts as a symmetry group. Give a closed cone \(\hat V\) in the dual of \({\mathbb{R}}^ d\). The representations of A are characterized having the properties: (i) The authomorphisms \(\alpha_ a\), \(a\in {\mathbb{R}}^ d\) are weakly inner, (ii) the corresponding unitary group representation U(a) is continuous and (iii) the spectrum of \(U(a)\) is contained in \(\hat V\).
Mathematics Subject Classification ID: 46L60
Mathematics Subject Classification ID: 46N99
Mathematics Subject Classification ID: 81T05
Mathematics Subject Classification ID: 46L55
Mathematics Subject Classification ID: 22D25
zbMATH DE Number: 3925598
zbMATH Keywords: translation group
zbMATH Keywords: spectrum condition
zbMATH Keywords: \(C^*\)-algebra
zbMATH Keywords: symmetry group
zbMATH Keywords: representations
zbMATH Keywords: weakly inner
zbMATH Keywords: unitary group representation
author: H. J. Borchers
MaRDI profile type: Publication
cites work: On groups of automorphisms of operator algebras
cites work: Q5833361
cites work: Q5800951
cites work: Energy and momentum as observables in quantum field theory
cites work: C*-algebras and automorphism groups
cites work: Covariance algebras in field theory and statistical mechanics
cites work: Q3205815
full work available at URL: https://doi.org/10.1007/bf01217346
OpenAlex ID: W2019716660
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description: scientific article; zbMATH DE number 3925598