Jiménez Fernández, Eduardo; Sánchez Pérez, Enrique Alfonso; Werner, Dirk(Institute of Mathematics, Polish Academy of Sciences, 2017-11-08)
[EN] We study whether or not the integration maps of vector measures can be
computed as pointwise limits of their finite rank Radon¿Nikodým derivatives. The positive
cases are obtained by using the circle of ideas related ...
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 ...
[EN] Requirements under which the Daugavet equation and the alternative Daugavet equation hold for pairs of nonlinear maps between Banach spaces are analyzed. A geometric description is given in terms of nonlinear slices. ...
Sánchez Pérez, Enrique Alfonso; Werner, Dirk(Duke University Press, 2011)
[EN] We show that Lp-spaces over atomless measure spaces can be
characterized in terms of a p-concavity type geometric property that is related
with the Daugavet property.
A natural extension of the Daugavet property for p-convex Banach function spaces and related classes is analysed. As an application, we extend the arguments given in the setting of the Daugavet property to show that no ...