The Daugavet equation for operators on function spaces

Abstract

We prove the norm identity $\|\Id+T\| =1+\|T\|$, which is known as the Daugavet equation, for weakly compact operators $T$ on natural function spaces such as function algebras and $L^1$-predual spaces, provided a non-discreteness assumption is met. We also consider $c_0$-factorable operators and operators on $C_{\Lambda }$-spaces.