Virtually free groups are $p$-Schatten stable

TL;DR

This paper proves that finitely generated virtually free groups exhibit stability under normalized p-Schatten norms, including Hilbert-Schmidt stability, contributing to the understanding of their approximation properties.

Contribution

It establishes the p-Schatten stability of finitely generated virtually free groups, a new result linking group theory and operator norm stability.

Findings

Virtually free groups are stable under normalized p-Schatten norms.

Virtually free groups are Hilbert-Schmidt stable.

The result applies for all 1 ≤ p < ∞.

Abstract

In this note we prove that finitely generated virtually free groups are stable with respect to a normalized $p$-Schatten norm for $1\leq p < \infty$. In particular, this implies that virtually free groups are Hilbert-Schmidt stable.