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The complete isomorphism class of an operator space


Author: Timur Oikhberg
Journal: Proc. Amer. Math. Soc. 135 (2007), 3943-3948
MSC (2000): Primary 46L07, 47L25
DOI: https://doi.org/10.1090/S0002-9939-07-08993-9
Published electronically: June 20, 2007
MathSciNet review: 2341944
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Abstract: Suppose $ X$ is an infinite-dimensional operator space and $ n$ is a positive integer. We prove that for every $ C > 0$ there exists an operator space $ \tilde{X}$ such that the formal identity map $ id : X \to \tilde{X}$ is a complete isomorphism, $ I_{\mathbf{M}_n} \otimes id$ is an isometry, and $ d_{cb}(X, \tilde{X}) > C$. This provides a non-commutative counterpart to a recent result of W. Johnson and E. Odell.


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Additional Information

Timur Oikhberg
Affiliation: Department of Mathematics, University of California, Irvine, Irvine, California 92697
Email: toikhber@math.uci.edu

DOI: https://doi.org/10.1090/S0002-9939-07-08993-9
Keywords: Exact operator space, complete isomorphism, c.b.~distance
Received by editor(s): June 28, 2006
Received by editor(s) in revised form: October 31, 2006
Published electronically: June 20, 2007
Additional Notes: The author was partially supported by the NSF grant DMS-0500957
Communicated by: N. Tomczak-Jaegermann
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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