Weak Baire measurability of the balls in a Banach space

José Rodríguez. "Weak Baire measurability of the balls in a Banach space." Studia Mathematica 185.2 (2008): 169-176. <http://eudml.org/doc/286577>.

@article{JoséRodríguez2008,
abstract = {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 $ℓ^\{∞\}(ℕ)$ 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.},
author = {José Rodríguez},
journal = {Studia Mathematica},
keywords = {Banach space; weak-separability; Baire -algebra; scalar measurability; Pettis integral},
language = {eng},
number = {2},
pages = {169-176},
title = {Weak Baire measurability of the balls in a Banach space},
url = {http://eudml.org/doc/286577},
volume = {185},
year = {2008},
}

TY - JOUR
AU - José Rodríguez
TI - Weak Baire measurability of the balls in a Banach space
JO - Studia Mathematica
PY - 2008
VL - 185
IS - 2
SP - 169
EP - 176
AB - 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 $ℓ^{∞}(ℕ)$ 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.
LA - eng
KW - Banach space; weak-separability; Baire -algebra; scalar measurability; Pettis integral
UR - http://eudml.org/doc/286577
ER -