This is an announcement for the paper "Weak-star point of continuity property and Schauder bases" by Gines Lopez Perez and Jose A. Soler Arias.

Abstract: We characterize the weak-star point of continuity property for subspaces of dual spaces with separable predual and we deduce that the weak-star point of continuity property is determined by subspaces with a Schauder basis in the natural setting of dual spaces of separable Banach spaces. As a consequence of the above characterization we get that a dual space satisfies the Radon-Nikodym property if, and only if, every seminormalized topologically weak-star null tree has a boundedly complete branch, which improves some results in \cite{DF} obtained for the separable case. Also, as a consequence of the above characterization, the following result obtained in \cite{R1} is deduced: {\it every seminormalized basic sequence in a Banach space with the point of continuity property has a boundedly complete subsequence

Archive classification: math.FA

Submitted from: glopezp@ugr.es

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1309.3862

or

http://arXiv.org/abs/1309.3862