This is an announcement for the paper "The Daugavet property of $C^*$-algebras, $JB^*$-triples, and of their isometric preduals" by Julio Becerra-Guerrero and Miguel Martin.

Abstract: A Banach space $X$ is said to have the Daugavet property if every rank-one operator $T:X\longrightarrow X$ satisfies $|Id + T| = 1 + |T|$. We give geometric characterizations of this property in the settings of $C^*$-algebras, $JB^*$-triples and their isometric preduals. We also show that, in these settings, the Daugavet property passes to ultrapowers, and thus, it is equivalent to an stronger property called the uniform Daugavet property.

Archive classification: Functional Analysis; Operator Algebras

Mathematics Subject Classification: Primary 17C; 46B04; 46B20; 46L05; 46L70; Secondary 46B22, 46M07

Remarks: 18 pages

The source file(s), BeceMart.tex: 68626 bytes, is(are) stored in gzipped form as 0407214.gz with size 19kb. The corresponding postcript file has gzipped size 90kb.

Submitted from: mmartins@ugr.es

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