\(C^*\)-algebras, Gelfand-Kirillov dimension, and Følner sets
type: Item
instance of: scholarly article
title: \(C^*\)-algebras, Gelfand-Kirillov dimension, and Følner sets
zbMATH Open document ID: 0973.46045
author: A. Y. Samet-Vaillant
published in: Journal of Functional Analysis
publication date: 2001-11-20T00:00:00Z
review text: It is shown that the set of asymptotic growth types of a finitely generated \(C^*\)-algebra is either completely polynomial, completely exponential, or mixed while containing exponential growth types. Further, it is shown that a finitely generated \(C^*\)-algebra has only completely polynomial growth types if and only if, for some \(n\in{\mathbb{N}}\), it can be imbedded into the algebra of \(n\times n\) matrices over a commutative \(C^*\)-algebra. Some of the results are extended to non finitely generated \(C^*\)-algebras.
Mathematics Subject Classification ID: 46L05
zbMATH DE Number: 1437357
zbMATH Keywords: \(C^*\)-algebra
zbMATH Keywords: asymptotic growth type
MaRDI profile type: Publication
full work available at URL: jfan.1999.3525
OpenAlex ID: W2033116635
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DOI: 10.1006/JFAN.1999.3525
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description: scientific article; zbMATH DE number 1437357