Crossed products of locally C*-algebras and Morita equivalence

TL;DR

This paper extends Morita equivalence concepts to group actions on locally C*-algebras, showing that strongly Morita equivalent actions produce strongly Morita equivalent crossed products, generalizing previous results.

Contribution

It introduces strong Morita equivalence for group actions on locally C*-algebras and proves the preservation of this equivalence in their crossed products.

Findings

Crossed products of strongly Morita equivalent actions are themselves strongly Morita equivalent.

Generalization of classical Morita equivalence results to locally C*-algebras.

Extension of Morita theory to inverse limit actions on locally C*-algebras.

Abstract

We introduce the notion of strong Morita equivalence for group actions on locally C*-algebras and prove that the crossed products associated with two strongly Morita equivalent continuous inverse limit actions of a locally compact group G on the locally C*-algebras A and B are strongly Morita equivalent. This generalizes a result of F. Combes, Proc. London Math. Soc. 49(1984) and R. E. Curto, P.S. Muhly, D. P. Williams, Proc. Amer. Soc. 90(1984).