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

Miguel Martin
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Abstract

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 $ω$ such that $\|Id + ωT\|= 1 + \|T\|$. We give geometric characterizations of this property in the setting of $C^*$-algebras, $JB^*$-triples and their isometric preduals.

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Miguel Martin. 2004-11-24. The Alternative Daugavet Property of $C^*$-algebras and $JB^*$-triples. https://arxiv.org/abs/math/0411555

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