Bimodule maps from a unital C^*-algebra to its C^*-subalgebra and strong Morita equivalence

2020/01/28 by Kazunori Kodaka, Kodaka, Kazunori
Mathematics · #46L05 #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.2001.10136

openalex publication_date 2020/01/28 · openalex created_date 2020/02/07 · openalex updated_date 2026/07/28

Abstract

Let A ⊂ C and B ⊂ D be unital inclusions of unital C^*-algebras. Let _A B_A (C, A) (resp. _B B_B (D, B)) be the space of all bounded A-bimodule (resp. B-bimodule) linear maps from C (resp. D) to A (resp. B). We suppose that A ⊂ C and B ⊂ D are strongly Morita equivalent. We shall show that there is an isometric isomorphism f of _A B_A (C, A) onto _B B_B (D, B) and we shall study on basic properties about f.

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