Let X be a Banach space. The property (∗) “the unit ball of X belongs to Baire(X, weak)” holds whenever the unit ball of X* is weak*-separable; on the other hand, it is also known that the validity of (∗) ensures that X* is weak*-separable. In this paper we use suitable renormings of and the Johnson-Lindenstrauss spaces to show that (∗) lies strictly between the weak*-separability of X* and that of its unit ball. As an application, we provide a negative answer to a question raised by K. Musiał.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm185-2-5,
author = {Jos\'e Rodr\'\i guez},
title = {Weak Baire measurability of the balls in a Banach space},
journal = {Studia Mathematica},
volume = {187},
year = {2008},
pages = {169-176},
zbl = {1147.46016},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm185-2-5}
}
José Rodríguez. Weak Baire measurability of the balls in a Banach space. Studia Mathematica, Tome 187 (2008) pp. 169-176. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm185-2-5/