The Alternative Daugavet Property of $C^*$-algebras and $JB^*$-triples

Details The Alternative Daugavet Property of $C^*$-algebras and $JB^*$-triples The Alternative Daugavet Property of $C^*$-algebras and $JB^*$-triples

2004-11-24

arxiv.org/abs/math/0411555v1

Mathematics

Functional Analysis

Scientific paper

A Banach space $X$ is said to have the alternative Daugavet property if for
every (bounded and linear) rank-one operator $T:X\longrightarrow X$ there
exists a modulus one scalar $\omega$ such that $\|Id + \omega T\|= 1 + \|T\|$.
We give geometric characterizations of this property in the setting of
$C^*$-algebras, $JB^*$-triples and their isometric preduals.

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