Ultraproducts of crossed product C*algebras

TL;DR

This paper investigates the relationship between ultraproducts of crossed product C*-algebras and crossed products of ultraproduct C*-algebras, providing insights into their structural connections.

Contribution

It establishes a detailed analysis of how ultraproducts and crossed products interact in the context of C*-algebras, highlighting new structural properties.

Findings

Identifies conditions under which $(A\rtimes_{r}G)^{\omega}$ and $A^{\omega}\rtimes_{r}G$ are related.

Provides structural theorems connecting ultraproducts and crossed products.

Enhances understanding of ultraproduct constructions in operator algebras.

Abstract

We study the relationship between the ultraproduct of a crossed product C*algebra $(A\rtimes_{r}G)^{\omega}$ and the crossed product of an ultraproduct C*algebra $A^{\omega}\rtimes _{r}G$ for a fixed free ultrafilter $\omega$ on $\mathbb{N}$.