Journal of Operator Theory

Volume 48, Issue 2, Fall 2002 pp. 447-451.

The flip is often discontinuous

Authors: Volker Runde
Author institution: Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta T6G 2G1, Canada

Summary: Let

$\A$ be a Banach algebra. The flip on

$\A \tensor \A^\op$ is defined through

$\A \tensor \A^\op \ni a \tensor b \mapsto b \tensor a$ . If

$\A$ is ultraprime,

$\El(\A)$ , the algebra of all eleme ntary operators on

$\A$ , can be algebraically identified with

$\A \tensor \A^\op$ , so that the flip is well defi ned on

$\El(\A)$ . We show that the flip on

$\El(\A)$ is discontinuous if

$\A = {\cal K}(E)$ for a reflexive Ban ach space

$E$ with the approximation property.

Contents Full-Text PDF