[Banach] Abstract of a paper by Julio Becerra-Guerrero and Miguel Martin

[Dale Alspach]

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 at ugr.es

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