Vol. 293, No. 2, 2018

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ISSN: 0030-8730
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

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.

von Neumann algebras, nonselfadjoint operator algebras, Kadison–Kastler metric, dual operator space, normal Haagerup tensor product, amenability
Mathematical Subject Classification 2010
Primary: 46L07, 47L55
Received: 1 July 2016
Revised: 10 April 2017
Accepted: 10 April 2017
Published: 23 November 2017
Jean Roydor
Institut de Mathématiques de Bordeaux
Université Bordeaux 1
351 Cours de la Libération
33405 Bordeaux Talence Cedex