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C*-algebras generated by mappings

Authors
  • Grigoryan, S.1
  • Kuznetsova, A.1
  • 1 Kazan State University, Kremlevskaya 18, Kazan, 420008, Russia , Kazan (Russia)
Type
Published Article
Journal
Lobachevskii Journal of Mathematics
Publisher
Pleiades Publishing
Publication Date
Jan 01, 2008
Volume
29
Issue
1
Pages
5–8
Identifiers
DOI: 10.1134/S1995080208010022
Source
Springer Nature
Keywords
License
Yellow

Abstract

Let X be an infinite set and let φ be a given mapping of it into itself. We consider the C*-algebra Cφ(X) with a single generating element Tφ on Hilbert space l2(X). We show that Cφ(X) is isomorphic to C*-algebra generated by a finite set of partial isometries of a special kind if Tφ is continuous. We give the full description of Cφ(X) in case φ is injective mapping. Also we give the examples of Cφ(X) if φ is not injective.

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