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Strong morita equivalence for conditional expectations

Part of: Selfadjoint operator algebras

Published online by Cambridge University Press:  08 February 2022

Kazunori Kodaka Open the ORCID record for Kazunori Kodaka [Opens in a new window]
Kazunori Kodaka*
Affiliation:
Department of Mathematical Sciences, Faculty of Science, Ryukyu University, Nishihara-cho, Okinawa903-0213, Japan (kodaka@math.u-ryukyu.ac.jp)
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Abstract

We consider two inclusions of $C^{*}$-algebras whose small $C^{*}$-algebras have approximate units of the large $C^{*}$-algebras and their two spaces of all bounded bimodule linear maps. We suppose that the two inclusions of $C^{*}$-algebras are strongly Morita equivalent. In this paper, we shall show that there exists an isometric isomorphism from one of the spaces of all bounded bimodule linear maps to the other space and we shall study the basic properties about the isometric isomorphism. And, using this isometric isomorphism, we define the Picard group for a bimodule linear map and discuss the Picard group for a bimodule linear map.

Keywords

bimodule mapsinclusions of C*-algebrasconditional expectationsstrong Morita equivalence

MSC classification

Primary: 46L05: General theory of $C^*$-algebras
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 65 , Issue 1 , February 2022 , pp. 182 - 213
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Copyright
Copyright © The Author(s), 2022. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society

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