The complete isomorphism class of an operator space
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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.References
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Additional Information
- Timur Oikhberg
- Affiliation: Department of Mathematics, University of California, Irvine, Irvine, California 92697
- MR Author ID: 361072
- Email: toikhber@math.uci.edu
- 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
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 2341944