Weak Baire measurability of the balls in a Banach space

被引：6

作者：

Rodriguez, Jose ^{[1
]}

机构：

[1] Univ Valencia, Dept Anal Matemat, E-46100 Valencia, Spain

来源：

STUDIA MATHEMATICA | 2008年 / 185卷 / 02期

关键词：

Banach space; weak*-separability; Baire sigma-algebra; scalar measurability; Pettis integral;

D O I：

10.4064/sm185-2-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let X be a Banach space. The property (star) "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 (star) ensures that X* is weak*-separable. In this paper we use suitable renormings of l(infinity) (N) and the Johnson-Lindenstrauss spaces to show that (star) 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. Musial.

引用

页码：169 / 176

页数：8

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