Toeplitz exactness for strong convergence

TL;DR

This paper introduces a new Toeplitz exactness theorem that enhances strong convergence in $C^*$-correspondences, with multiple applications in operator algebra theory.

Contribution

The paper presents a novel Toeplitz exactness theorem that improves the understanding of strong convergence in $C^*$-correspondences.

Findings

Establishes a new method to upgrade strong convergence.

Provides applications demonstrating the theorem's utility.

Abstract

We prove a new "Toeplitz exactness" theorem for strong convergence. This is a machine to upgrade strong convergence in the general setting of $C^\ast$-correspondences, and has several applications.