A non-commutative Amir-Cambern theorem for von Neumann algebras and nuclear C^*-algebras

2011/08/09 by Éric Ricard, Ricard, Eric, Jean Roydor +1
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1108.1970

openalex publication_date 2011/08/09 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We prove that von Neumann algebras and separable nuclear C^*-algebras are stable for the Banach-Mazur cb-distance. A technical step is to show that unital almost completely isometric maps between C^*-algebras are almost multiplicative and almost selfadjoint. Also as an intermediate result, we compare the Banach-Mazur cb-distance and the Kadison-Kastler distance. Finally, we show that if two C^*-algebras are close enough for the cb-distance, then they have at most the same length.

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