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THE STRONG MORITA EQUIVALENCE FOR INCLUSIONS OF $C^{\ast }$-ALGEBRAS AND CONDITIONAL EXPECTATIONS FOR EQUIVALENCE BIMODULES

Part of: Selfadjoint operator algebras

Published online by Cambridge University Press:  12 December 2017

KAZUNORI KODAKA Open the ORCID record for KAZUNORI KODAKA [Opens in a new window]  and
TAMOTSU TERUYA
KAZUNORI KODAKA*
Affiliation:
Department of Mathematical Sciences, Faculty of Science, Ryukyu University, Nishihara-cho, Okinawa, 903-0213, Japan email kodaka@math.u-ryukyu.ac.jp
TAMOTSU TERUYA
Affiliation:
Faculty of Education, Gunma University, 4-2 Aramaki-machi, Maebashi City, Gunma, 371-8510, Japan
*
✉kodaka@math.u-ryukyu.ac.jp
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Abstract

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We shall introduce the notions of strong Morita equivalence for unital inclusions of unital $C^{\ast }$-algebras and conditional expectations from an equivalence bimodule onto its closed subspace with respect to conditional expectations from unital $C^{\ast }$-algebras onto their unital $C^{\ast }$-subalgebras. Also, we shall study their basic properties.

Keywords

inclusions of C∗ -algebrasstrong Morita equivalenceequivalence bimodulesconditional expectations

MSC classification

Primary: 46L05: General theory of $C^*$-algebras
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 105 , Issue 1 , August 2018 , pp. 103 - 144
Copyright
© 2017 Australian Mathematical Publishing Association Inc. 

References

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
Brown, L. G., Mingo, J. and Shen, N.-T., ‘Quasi-multipliers and embeddings of Hilbert C ∗ -bimodules’, Canad. J. Math. 46 (1994), 1150–1174.CrossRefGoogle Scholar
Jansen, S. and Waldmann, S., ‘The H-covariant strong Picard groupoid’, J. Pure Appl. Algebra 205 (2006), 542–598.CrossRefGoogle Scholar
Kajiwara, T. and Watatani, Y. , ‘Jones index theory by Hilbert C ∗ -bimodules and K-theory’, Trans. Amer. Math. Soc. 352 (2000), 3429–3472.CrossRefGoogle Scholar
Kodaka, K. and Teruya, T., ‘The strong Morita equivalence for coactions of a finite dimensional C ∗ -Hopf algebra on unital C ∗ -algebras’, Studia Math. 228 (2015), 259–294.CrossRefGoogle Scholar
Osaka, H., Kodaka, K. and Teruya, T., ‘The Rohlin property for inclusions of C ∗ -algebras with a finite Watatani index’, in: Operator Structures and Dynamical Systems, Contemporary Mathematics, 503 (American Mathematical Society, Providence, RI, 2009), 177–195.CrossRefGoogle Scholar
Raeburn, I. and Williams, D. P., Morita Equivalence and Continuous-Trace C ∗ -Algebras, Mathematical Surveys and Monographs, 60 (American Mathematical Society, Providence, RI, 1998).CrossRefGoogle Scholar
Rieffel, M. A., ‘ C ∗ -algebras associated with irrational rotations’, Pacific J. Math. 93 (1981), 415–429.CrossRefGoogle Scholar
Tomiyama, J., ‘On the projection of norm one in W ∗ -algebras’, Proc. Japan Acad. Ser. A Math. Sci. 33 (1957), 608–612.CrossRefGoogle Scholar
Watatani, Y., ‘Index for C ∗ -subalgebras’, Mem. Amer. Math. Soc. 424 (1990).Google Scholar