Ultraproducts of crossed product von Neumann algebras

TL;DR

This paper explores the relationship between ultraproducts and crossed product von Neumann algebras, providing insights into their structure and describing the continuous core of ultraproducts.

Contribution

It establishes a connection between ultraproducts of crossed products and crossed products of ultraproducts, advancing understanding of von Neumann algebra structures.

Findings

Describes the continuous core of ultraproduct von Neumann algebras

Establishes a relationship between ultraproducts and crossed products

Provides tools for analyzing ultraproduct von Neumann algebras

Abstract

We study a relationship between the ultraproduct of a crossed product von Neumann algebra and the crossed product of an ultraproduct von Neumann algebra. As an application, the continuous core of an ultraproduct von Neumann algebra is described.