A non-commutative Amir-Cambern theorem for von Neumann algebras and nuclear $C^*$-algebras
作者： Eric Ricard , Jean Roydor
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摘要: 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 unital almost completely isometric maps between multiplicative selfadjoint. Also as an intermediate result, we compare cb-distance Kadison-Kastler distance. Finally, if two close enough cb-distance, then they have at most same length.
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Christian Le Merdy, David P. Blecher, Operator Algebras and Their Modules: An Operator Space Approach ,(2005)
Gilles Pisier, Introduction to Operator Space Theory ,(2003)
Vern I. Paulsen, Completely Bounded Maps and Operator Algebras ,(2003)
Gilles Pisier, The similarity degree of an operator algebra, II Mathematische Zeitschrift. ,vol. 235, pp. 53- 82 ,(2000) , 10.1007/S002090050503
L. Terrell Gardner, A note on isomorphisms of $C^*$-algebras Bulletin of the American Mathematical Society. ,vol. 70, pp. 788- 791 ,(1964) , 10.1090/S0002-9904-1964-11238-6
B. E. Johnson, Perturbations of Banach Algebras Proceedings of the London Mathematical Society. ,vol. s3-34, pp. 439- 458 ,(1977) , 10.1112/PLMS/S3-34.3.439
Iain Raeburn, Joseph L Taylor, Hochschild cohomology and perturbations of Banach algebras Journal of Functional Analysis. ,vol. 25, pp. 258- 266 ,(1977) , 10.1016/0022-1236(77)90072-6
Michael Cambern, On isomorphisms with small bound Proceedings of the American Mathematical Society. ,vol. 18, pp. 1062- 1066 ,(1967) , 10.1090/S0002-9939-1967-0217580-2
Erik Christensen, Allan Sinclair, Roger R. Smith, Stuart White, Perturbations of C*-algebraic invariants Geometric and Functional Analysis. ,vol. 20, pp. 368- 397 ,(2010) , 10.1007/S00039-010-0070-Y
D. Amir, On isomorphisms of continuous function spaces Israel Journal of Mathematics. ,vol. 3, pp. 205- 210 ,(1965) , 10.1007/BF03008398