This is an announcement for the paper "Slice continuity for operators and the Daugavet property for bilinear maps" by Enrique A. Sanchez Perez and Dirk Werner.
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.
Archive classification: math.FA
Mathematics Subject Classification: Primary 46B04, secondary 46B25
Submitted from: werner@math.fu-berlin.de
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1210.7099
or