A Morita equivalence for Hilbert C*-modules

TL;DR

This paper introduces a new Morita equivalence concept for Hilbert C*-modules based on the Morita equivalence of their compact operator algebras, with applications to group actions and Green's theorem extension.

Contribution

It defines Morita equivalence for Hilbert C*-modules via their compact operator algebras and explores its properties and applications.

Findings

Established properties of the new Morita equivalence

Extended Green's theorem to Hilbert C*-modules

Analyzed group actions on full Hilbert C*-modules

Abstract

In this paper we introduce a notion of Morita equivalence for Hilbert C*-modules in terms of the Morita equivalence of the algebras of compact operators on Hilbert C*-modules. We investigate some properties of the new version of Morita equivalence and obtain some results. We then applied our results to study the continuous actions of locally compact groups on full Hilbert C*-modules. We present an extension of Green's theorem in the context of Hilbert C*-modules as well.