THE STRONG MORITA EQUIVALENCE FOR INCLUSIONS OF C^∗ -ALGEBRAS AND CONDITIONAL EXPECTATIONS FOR EQUIVALENCE BIMODULES

We shall introduce the notions of the strong Morita equivalence for unital inclusions of unital C^*-algebras and conditional expectations from an equivalence bimodule onto its closed subspace with respect to conditional expectations from unital C^*-algebras onto their unital C^*-subalgebras. Also, we shall study their basic properties