Journal of Operator Theory

Volume 61, Issue 1, Winter 2009 pp. 3-18.

Finite representability of homogeneous Hilbertian operator spaces in spaces with few completely bounded maps

Authors: Timur Oikhberg
Author institution: Department of Mathematics, University of California - Irvine, Irvine CA 92697, USA

Summary: For every homogeneous Hilbertian operator space

$H$ , we construct a Hilbertian operator space

$X$ such that every infinite dimensional subquotient

$Y$ of

$X$ is completely indecomposable, and fails the Operator Approximation Property, yet

$H$ is completely finitely representable in

$Y$ . If

$H$ satisfies certain conditions, we also prove that every completely bounded map on such

$Y$ is a compact perturbation of a scalar.

Keywords: Operator spaces, homogeneous Hilbertian spaces, finite representability, Operator Approximation Property.

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