Induced representations of Hilbert $C^*$-modules

TL;DR

This paper introduces the concept of induced representations for Hilbert C*-modules and demonstrates that Morita equivalence between modules leads to equivalent categories of their non-degenerate representations.

Contribution

It defines induced representations for Hilbert C*-modules and establishes a link between Morita equivalence and categorical equivalence of their representations.

Findings

Morita equivalence implies categorical equivalence of representations

Introduces a new notion of induced representations for Hilbert modules

Establishes a theoretical connection between module equivalences and representation categories

Abstract

In this paper, we define the notion of induced representations of a Hilbert $C^{*}$-module and we show that Morita equivalence of two Hilbert modules (in the sense of Moslehian and Joita), implies the equivalence of categories of non-degenerate representations of two Hilbert modules.