Dual operator algebras close to injective von Neumann algebras

Jean Roydor

Vol. 293 (2018), No. 2, 407–426

DOI: 10.2140/pjm.2018.293.407

Abstract

We prove that if a nonselfadjoint dual operator algebra admitting a normal virtual diagonal and an injective von Neumann algebra are close enough for the Kadison–Kastler metric, then they are similar. The bound explicitly depends on the norm of the normal virtual diagonal. This is inspired by E. Christensen’s work on perturbation of operator algebras and is related to a conjecture of G. Pisier on nonselfadjoint amenable operator algebras.

Keywords

von Neumann algebras, nonselfadjoint operator algebras, Kadison–Kastler metric, dual operator space, normal Haagerup tensor product, amenability

Mathematical Subject Classification 2010

Primary: 46L07, 47L55

Milestones

Received: 1 July 2016

Revised: 10 April 2017

Accepted: 10 April 2017

Published: 23 November 2017