Morita equivalence of Hilbert $C^{*}$-modules

Abstract

We give a direct definition of Morita equivalence for Hilbert $C^{*}$ -modules, by introducing an explicit list of axioms for an imprimitivity bimodule. We show that Hilbert $C^{*}$-modules with unit vectors, over Morita equivalent unital $C^{*}$-algebras, are Morita equivalent, and Morita equivalence is an equivalence relation in the category of left Hilbert $C^{*} $-modules with unit vectors.