arXiv subjects

Enrique A. Sanchez Perez

Publications and source records attributed to Enrique A. Sanchez Perez.

4 recordsLinked to original sources

arXiv2017

Approximation of integration maps of vector measures and limit representations of Banach function spaces

We study when the integration maps of vector measures can be computed as pointwise limits of their finite rank Radon-Nikodým derivatives. We will show that this can sometimes be done, but there are also principal cases in which this cannot be done. The positive cases are obtained using the circle of ideas of the approximation property for Banach spaces. The negative ones are given by means of an adequate use of the Daugavet property. As an application, we analyse when the norm in a space of integrable functions $L^1(m)$ can be computed as a limit of the norms of the spaces of integrable functions with respect to the Radon-Nikodým derivatives of $m$.

math.FA↗

arXiv2015

The Daugavet equation for bounded vector valued functions

Requirements under which the Daugavet equation and the alternative Daugavet equation hold for pairs of nonlinear maps between Banach spaces are analysed. A geometric description is given in terms of nonlinear slices. Some local versions of these properties are also introduced and studied, as well as tests for checking if the required conditions are satisfied in relevant cases.

math.FA↗

arXiv2011

The $p$-Daugavet property for function spaces

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 reflexive space falls into this class.

math.FA↗

arXiv2010

The geometry of L^p-spaces over atomless measure spaces and the Daugavet property

We show that $L^p$-spaces over atomless measure spaces can be characterized in terms of a $p$-concavity type geometric property that is related with the Daugavet property.

math.FA↗