A noncommutative Amir-Cambern theorem for von Neumann algebras and nuclear ${C}^∗$-algebras.
RICARD, Éric
Laboratoire de Mathématiques de Besançon (UMR 6623) [LMB]
Laboratoire de Mathématiques Nicolas Oresme [LMNO]
Laboratoire de Mathématiques de Besançon (UMR 6623) [LMB]
Laboratoire de Mathématiques Nicolas Oresme [LMNO]
RICARD, Éric
Laboratoire de Mathématiques de Besançon (UMR 6623) [LMB]
Laboratoire de Mathématiques Nicolas Oresme [LMNO]
< Réduire
Laboratoire de Mathématiques de Besançon (UMR 6623) [LMB]
Laboratoire de Mathématiques Nicolas Oresme [LMNO]
Langue
en
Article de revue
Ce document a été publié dans
J. Funct. Anal. 267 (2014). 2014p. J. Funct. Anal. 267 (2014), no. 4, 1121-1136.
Résumé en anglais
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 ...Lire la suite >
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.< Réduire
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