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@ugr.es

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