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The complete isomorphism class of an operator space

Author(s): Timur Oikhberg
Journal: Proc. Amer. Math. Soc. 135 (2007), 3943-3948.
MSC (2000): Primary 46L07, 47L25
Posted: June 20, 2007
MathSciNet review: 2341944
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Abstract: Suppose is an infinite-dimensional operator space and is a positive integer. We prove that for every 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: 10.1090/S0002-9939-07-08993-9
PII: S 0002-9939(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
Posted: June 20, 2007
Additional Notes: The author was partially supported by the NSF grant DMS-0500957
Communicated by: N. Tomczak-Jaegermann
Copyright of article: Copyright 2007, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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