This is an announcement for the paper "The alternative Daugavet property of $C^*$-algebras and $JB^*$-triples" by Miguel Martin.

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 $\omega$ 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.

Archive classification: Functional Analysis; Operator Algebras

Mathematics Subject Classification: 46B20, 46L05, 17C65 (primary); 47A12 (secondary)

The source file(s), Martin-ADP.tex: 44541 bytes, is(are) stored in gzipped form as 0411555.gz with size 14kb. The corresponding postcript file has gzipped size 69kb.

Submitted from: mmartins@ugr.es

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http://front.math.ucdavis.edu/math.FA/0411555

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http://arXiv.org/abs/math.FA/0411555

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uget 0411555

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