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Partial automorphisms of stable C*-algebras and Hilbert C*-bimodules

Part of: Selfadjoint operator algebras

Published online by Cambridge University Press:  09 April 2009

Kazunori Kodaka
Kazunori Kodaka
Affiliation:
Department of Mathematical Sciences, Faculty of Science, Ryukyu University Nishihara-cho, Okinawa 903-0213, Japan, e-mail: [email protected]
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Abstract

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Let A be a C*-algebra and K the C*-algebra of all compact operators on a countably infinite dimensional Hilbert space. In this note, we shall show that there is an isomorphism of a semigroup of equivalence classes of certain partial automorphisms of A ⊗ K onto a semigroup of equivalence classes of certain countably generated A-A-Hilbert bimodules.

MSC classification

Secondary: 46L08: $C^*$-modules 46L40: Automorphisms
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 79 , Issue 3 , December 2005 , pp. 391 - 398
Copyright
Copyright © Australian Mathematical Society 2005

References

[1]Abadie, B., Eilers, S. and Exel, R., ‘Morita equivalence for crossed products by Hilbert C*-bimodules’, Trans. Amer. Math. Soc. 350 (1998), 3043–3054.CrossRefGoogle Scholar
[2]Blackadar, B., K-theory for operator algebras, Mathematical Sciences Research Institute Publications 5, 2nd Edition (Cambridge Univ. Press, Cambridge, 1998).Google Scholar
[3]Brown, L. G., ‘Stable isomorphism of hereditary subalgebras of C*-algebras’, Pacific J. Math. 71 (1977), 335–348.CrossRefGoogle Scholar
[4]Brown, L. G., Green, P. and Rieffel, M. A., ‘Stable isomorphism and strong Morita equivalence of C*-algebras’, Pacific J. Math. 71 (1977), 349–363.CrossRefGoogle Scholar
[5]Brown, L. G., Mingo, J. A. and Shen, N., ‘Quasi-multipliers and embeddings of Hilbert C*-bimodules’, Canad. J. Math. 46 (1994), 1150–1174.CrossRefGoogle Scholar
[6]Exel, R., ‘Circle actions on C*-algebras, partial automorphisms and a generalized Pimzner-Voiculescu exact sequence’, J. Funct. Anal. 122 (1994), 361–401.CrossRefGoogle Scholar
[7]Jensen, K. K. and Thomsen, K., Elements of KK-theory (Birkäuser, 1991).CrossRefGoogle Scholar
[8]Pedersen, G. K., C*-algebras and their automorphism groups (Academic Press, 1979).Google Scholar