The Daugavet Equation for Operators on Function Spaces

• DOI: 10.1006/jfan.1996.2979
• Publication Date: 2002-10-06T17:40:27Z
• Authors: Dirk Werner
• Keywords: Function space

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 $C_��$-spaces.