Isometric Actions are Quasidiagonal

TL;DR

This paper proves that all isometric actions are quasidiagonal, implying that the associated reduced crossed products inherit quasidiagonality or MF properties if the group algebra has these properties.

Contribution

It establishes that every isometric action is quasidiagonal, linking group action properties to the structure of crossed product C*-algebras.

Findings

All isometric actions are quasidiagonal.

Reduced crossed products are quasidiagonal or MF if the group algebra is.

Connects group action properties with algebraic structures.

Abstract

We show every isometric action is quasidiagonal in a strong sense. This shows that reduced crossed products by such actions are quasidiagonal or MF whenever the reduced algebra of the acting group is quasidiagonal or MF.