Mathematische Annalen

, Volume 328, Issue 1–2, pp 229–259 | Cite as

Operator spaces with few completely bounded maps

  • Timur OikhbergEmail author
  • Éric Ricard


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 \({{T : X {{\rightarrow}} X'}}\) is a completely bounded map, then TI X +S, where S is compact Hilbert-Schmidt and ||S||2/16≤||S|| cb ≤||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.


Banach Space Operator Space Approximation Property Operator Approximation Space Structure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of California at IrvineIrvineUSA
  2. 2.Département de Mathématiques de BesançonUniversité de Franche-ComtéFrance

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