The complete isomorphism class of an operator space

Oikhberg, Timur

doi:10.1090/S0002-9939-07-08993-9

The complete isomorphism class of an operator space
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Proc. Amer. Math. Soc. 135 (2007), 3943-3948 Request permission

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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