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# 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.

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