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 show that a dual space has the Radon-Nikodym property if, and only if, every seminormalized topologically weak-star null tree has a boundedly complete branch, which improves some results of Dutta and Fonf (2008) obtained for the separable case. Also, as a consequence of the above characterization, the following result of Rosenthal (2007) is deduced: every seminormalized basic sequence in a Banach space with the point of continuity property has a boundedly complete subsequence.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm219-3-3,
author = {Gin\'es L\'opez-P\'erez and Jos\'e A. Soler-Arias},
title = {Weak-star point of continuity property and Schauder bases},
journal = {Studia Mathematica},
volume = {215},
year = {2013},
pages = {225-236},
zbl = {1294.46013},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm219-3-3}
}
Ginés López-Pérez; José A. Soler-Arias. Weak-star point of continuity property and Schauder bases. Studia Mathematica, Tome 215 (2013) pp. 225-236. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm219-3-3/