Strong morita equivalence for conditional expectations. Issue 1 (8th February 2022)

• Record Type: Journal Article
• Authors: Kodaka, Kazunori
• Is Part Of: Proceedings of the Edinburgh Mathematical Society. Volume 65:Issue 1(2022)
• Page Start: 182
• Page End: 213
• Publication Date: 2022-02-08
• Subjects: bimodule maps -- inclusions of C*-algebras -- conditional expectations -- strong Morita equivalence; 46L05; Mathematics -- Periodicals; 510
• DOI: 10.1017/S0013091522000025
• Languages: English
• ISSNs: 0013-0915

Abstract

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.