Dual operator algebras close to injective von Neumann algebras

TL;DR

This paper demonstrates that dual operator algebras with a normal virtual diagonal, when sufficiently close to injective von Neumann algebras in the Kadison-Kastler metric, are similar, extending Christensen's perturbation results.

Contribution

It establishes a quantitative similarity result for dual operator algebras near injective von Neumann algebras, incorporating the role of the normal virtual diagonal.

Findings

Proves similarity under Kadison-Kastler proximity

Provides explicit bounds based on the normal virtual diagonal

Extends Christensen's perturbation theory to a broader class of algebras

Abstract

We prove that if a non-selfadjoint dual operator algebra admitting a normal virtual diagonal and an injective von Neumann algebra are close enough for the Kadison-Kastler's metric, then they are similar. The bound explicitly depends on the norm of the normal virtual diagonal. This is inspired from E. Christensen's work on perturbation of operator algebras.