Proceedings of the Edinburgh Mathematical Society (Series 2)

Research Article

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

Narutaka Ozawaa1

a1 Texas A&M University, College Station, TX77843, USA and University of Tokyo, Komaba, 153-8914, Japan (ozawa@math.tamu.edu)

Abstract

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

(Received September 10 1999)

Keywords

  • bounded linear extensions;
  • non-exact Q-spaces