Morita equivalence and Cauchy extensions of Hilbert C*-modules

Abstract

In this paper, we show that the Cauchy extensions of C*-algebras and Hilbert C*-modules preserve Morita equivalence of C*-algebras and Hilbert C*- modules, respectively. In particular, we show that the Cauchy extensions of Hilbert C*-modules preserve adjointable, unitary operators and partial isometries as well as full Hilbert C*-modules and linking algebras associated to Hilbert C*-modules.