Induced representations of Hilbert modules over locally C*-algebras and the imprimitivity theorem

TL;DR

This paper explores how induced representations of Hilbert modules over locally C*-algebras relate under Morita equivalence, establishing a bijective correspondence between their non-degenerate representations.

Contribution

It demonstrates a new correspondence between representations of Morita equivalent Hilbert modules over locally C*-algebras.

Findings

Existence of a bijective correspondence between representations of Morita equivalent modules

Non-degeneracy of induced representations is preserved

Extension of imprimitivity theorem to locally C*-algebra modules

Abstract

We study induced representations of Hilbert modules over locally C*-algebras and their non-degeneracy. We show that if $V$ and $W$ are Morita equivalent Hilbert modules over locally C*-algebras $A$ and $B$, respectively, then there exists a bijective correspondence between equivalence classes of non-degenerate representations of $V$ and $W$.