%0 Journal Article
%T A non-commutative Amir-Cambern theorem for von Neumann algebras and nuclear $C^*$-algebras
%A Eric Ricard
%A Jean Roydor
%J Mathematics
%D 2011
%I arXiv
%X 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.
%U http://arxiv.org/abs/1108.1970v2