This is an announcement for the paper “Lipschitz slices versus linear slices in Banach spaces” by Julio Becerra Guerrero, Gines Lopez-Perez and Abraham Rueda Zoca.

Abstract: The aim of this note is study the topology generated by Lipschitz slices in the unit sphere of a Banach space. We prove that the above topology agrees with the weak topology in the unit sphere and, as a consequence, we obtain Lipschitz characterizations of classical linear topics in Banach spaces, as Radon-Nikodym property, convex point of continuity property and strong regularity, which shows that the above classical linear properties only depend on the natural uniformity in the Banach space given by the metric and the linear structure.

The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1604.04430