Abstract
We introduce and analyse the notion of slice continuity between operators on Banach
spaces in the setting of the Daugavet property. It is shown that under the slice continuity
assumption the Daugavet equation holds for weakly compact operators. As an application we
define and characterise the Daugavet property for bilinear maps, and we prove that this allows us
to describe some p-convexifications of the Daugavet equation for operators on Banach function
spaces that have recently been introduced.
