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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. 

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