The strong Morita equivalence for inclusions of $C^{\ast }$-algebras and conditional expectations for equivalence bimodules

Abstract

We shall introduce the notions of the 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.

35pages

Cited by in corpus (1)

• Coactions of a finite dimensional $C^{\ast }$-Hopf algebra on unital $C^{\ast }$-algebras, unital inclusions of unital $C^{\ast }$-algebras and the strong Morita equivalence