Group actions on pro-$C^{*}$-algebras and their pro-$C^{*}$-crossed products

TL;DR

This paper introduces the concepts of full and reduced pro-$C^{*}$-crossed products for pro-$C^{*}$-algebras under group actions and explores their fundamental properties.

Contribution

It defines new types of crossed products for pro-$C^{*}$-algebras and studies their key properties, advancing the understanding of group actions in this context.

Findings

Defined full and reduced pro-$C^{*}$-crossed products.

Analyzed properties of these crossed products.

Extended classical concepts to the pro-$C^{*}$-algebra setting.

Abstract

In this paper, we define the notions of full pro-$C^{*}$-crossed product, respectively reduced pro-$C^{*}$-crossed product, of a pro-$C^{*}$-algebra $A[\tau_{\Gamma}] $ by a strong bounded action $\alpha$ of a locally compact group $G$ and investigate some their properties.