  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.
