Abstract
We consider theC*-algebra\(\mathcal{O}_n \) generated byn≧2 isometriesS 1,...,S n on an infinite-dimensional Hilbert space, with the property thatS 1 S*1+...+S n S* n =1. It turns out that\(\mathcal{O}_n \) has the structure of a crossed product of a finite simpleC*-algebra ℱ by a single endomorphism scaling the trace of ℱ by 1/n. Thus,\(\mathcal{O}_n \) is a separableC*-algebra sharing many of the properties of a factor of typeIII λ with λ=1/n. As a consequence we show that\(\mathcal{O}_n \) is simple and that its isomorphism type does not depend on the choice ofS 1,...,S n .
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Communicated by H. Araki
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Cuntz, J. SimpleC*-algebra generated by isometries. Commun.Math. Phys. 57, 173–185 (1977). https://doi.org/10.1007/BF01625776
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DOI: https://doi.org/10.1007/BF01625776