Weak-star point of continuity property and Schauder bases
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
Keywords
Cite
@article{arxiv.1309.3862,
title = {Weak-star point of continuity property and Schauder bases},
author = {Ginés López Pérez and José A. Soler Arias},
journal= {arXiv preprint arXiv:1309.3862},
year = {2013}
}