An elementary approach to the Daugavet equation

Details An elementary approach to the Daugavet equation An elementary approach to the Daugavet equation

1994-12-12

arxiv.org/abs/math/9412212v1

Lect. Notes Pure Appl. Math. 175, 449-454 (1996)

Mathematics

Functional Analysis

Scientific paper

Let $T\dopu C(S)\to C(S)$ be a bounded linear operator. We present a
necessary and sufficient condition for the so-called Daugavet equation $$
\|\Id+T\| = 1+\|T\| $$ to hold, and we apply it to weakly compact operators and
to operators factoring through $c_{0}$. Thus we obtain very simple proofs of
results by Foias, Singer, Pelczynski, Holub and others.

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