Weak-star point of continuity property and Schauder bases

Ginés López-Pérez, and José A. Soler-Arias. "Weak-star point of continuity property and Schauder bases." Studia Mathematica 219.3 (2013): 225-236. <http://eudml.org/doc/285497>.

@article{GinésLópez2013,
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 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.},
author = {Ginés López-Pérez, José A. Soler-Arias},
journal = {Studia Mathematica},
keywords = {point of continuity property; trees; boundedly complete sequences},
language = {eng},
number = {3},
pages = {225-236},
title = {Weak-star point of continuity property and Schauder bases},
url = {http://eudml.org/doc/285497},
volume = {219},
year = {2013},
}

TY - JOUR
AU - Ginés López-Pérez
AU - José A. Soler-Arias
TI - Weak-star point of continuity property and Schauder bases
JO - Studia Mathematica
PY - 2013
VL - 219
IS - 3
SP - 225
EP - 236
AB - 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.
LA - eng
KW - point of continuity property; trees; boundedly complete sequences
UR - http://eudml.org/doc/285497
ER -