Journal of Operator Theory

Volume 39, Issue 1, Winter 1998 pp. 89-98.

The Daugavet equation for operators not fixing a copy of

$\scriptstyle C[0,1]$

Authors: Lutz Weis (1), and Dirk Werner (2)
Author institution: (1) Mathematisches Institut I, Universit\"at Karlsruhe, D-76128 Karlsruhe, Germany
(2) I. Mathematisches Institut, Freie Universit\"at Berlin, Arnimallee 2--6, D-14195 Berlin, Germany

Summary: We prove the norm identity

$\|{\rm Id}+T\| = 1+\|T\|$ , which is known as the Daugavet equation, for operators

$T$ on

$C(S)$ not fixing a copy of

$C[0,1]$ , where

$S$ is a compact Hausdorff space without isolated points.

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