[Banach] Abstract of a paper by Vladimir Kadets, Miguel Martin, and Javier Meri

[Dale Alspach]

This is an announcement for the paper "Norm equalities for operators"
by Vladimir Kadets, Miguel Martin, and Javier Meri.


Abstract: A Banach space $X$ has the Daugavet property if the
Daugavet equation $\|\Id + T\|= 1 + \|T\|$ holds for every rank-one
operator $T:X \longrightarrow X$. We show that the most natural
attempts to introduce new properties by considering other norm
equalities for operators (like $\|g(T)\|=f(\|T\|)$ for some functions
$f$ and $g$) lead in fact to the Daugavet property of the space.
On the other hand there are equations (for example $\|\Id + T\|=
\|\Id - T\|$) that lead to new, strictly weaker properties of Banach
spaces.

Archive classification: Functional Analysis

Mathematics Subject Classification: 46B20

Remarks: 21 pages

The source file(s), KadMarMer.tex: 56515 bytes, is(are) stored in
gzipped form as 0604102.gz with size 17kb. The corresponding postcript
file has gzipped size 87kb.

Submitted from: mmartins at ugr.es

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 http://front.math.ucdavis.edu/math.FA/0604102

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 http://arXiv.org/abs/math.FA/0604102

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