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.

Key words: Extension of C- algebras, extension of Hilbert C-modules, Cauchy extension of C- algebras, Morita equivalence.