The Daugavet property of $C^*$-algebras, $JB^*$-triples, and of their isometric preduals

Becerra-Guerrero, Julio; Martin, Miguel

The Daugavet property of $C^$-algebras, $JB^$-triples, and of their isometric preduals

Authors

Description

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.
To appear in J. Funct. Anal., final form, 19 pages