Mathematics – Functional Analysis
Scientific paper
2004-07-13
Mathematics
Functional Analysis
To appear in J. Funct. Anal., final form, 19 pages
Scientific paper
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.
Becerra-Guerrero Julio
Martin Miguel
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