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

Published online by Cambridge University Press:  20 January 2009

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

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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

Keywords

bounded linear extensionsnon-exact Q-spaces
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 44 , Issue 2 , June 2001 , pp. 241 - 248
Copyright
Copyright © Edinburgh Mathematical Society 2001