A NON-EXTENDABLE BOUNDED LINEAR MAP BETWEEN C*-ALGEBRAS

We present an example of a $C^*$-subalgebra $A$ of $\mathbb{B}(H)$ and a bounded linear map from $A$ to $\mathbb{B}(K)$ which does not admit any bounded linear extension. This generalizes the result of Robertson and gives the answer to a problem raised by Pisier. Using the same idea, we compute the exactness constants of some Q-spaces. This solves a problem raised by Oikhberg. We also construct a Q-space which is not locally reflexive.AMS 2000 Mathematics subject classification: Primary 46L05. Secondary 46L07