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Article Dans Une Revue Mathematische Annalen Année : 2004

Operator spaces with few completely bounded maps

Éric Ricard
Timur Oikhberg
  • Fonction : Auteur

Résumé

We construct several examples of Hilbertian operator spaces with few completely bounded maps. In particular, we give an example of a separable $1$-Hilbertian operator space $X_0$ such that, whenever $X'$ is an infinite dimensional quotient of $X_0$, $X$ is a subspace of $X'$, and $T : X \raw X'$ is a completely bounded map, then $T = \lambda I_{X} + S$, where $S$ is compact Hilbert-Schmidt and $||S||_2/16 \leq ||S||_{cb} \leq ||S||_2$. Moreover, every infinite dimensional quotient of a subspace of $X_0$ fails the operator approximation property. We also show that every Banach space can be equipped with an operator space structure without the operator approximation property.

Dates et versions

hal-00475252 , version 1 (21-04-2010)

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Citer

Éric Ricard, Timur Oikhberg. Operator spaces with few completely bounded maps. Mathematische Annalen, 2004, 328 (1-2), pp.229-259. ⟨10.1007/s00208-003-0481-2⟩. ⟨hal-00475252⟩
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