A weak Asplund space whose dual is not weak* fragmentable

被引：12

作者：

Kenderov, PS

Moors, WB

Sciffer, S

机构：

[1] Bulgarian Acad Sci, Inst Math, Sofia 1113, Bulgaria

[2] Univ Waikato, Dept Math, Hamilton, New Zealand

[3] Univ Newcastle, Dept Math, Newcastle, NSW 2308, Australia

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2001年 / 129卷 / 12期

关键词：

Stegall's class; fragmentability; weak Asplund space; double arrow space; Baire space; minimal usco;

D O I：

10.1090/S0002-9939-01-06002-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Under the assumption that there exists in the unit interval [0, 1] an uncountable set A with the property that every continuous mapping from a Baire metric space B into A is constant on some non-empty open subset of B, we construct a Banach space X such that (X*; weak*) belongs to Stegall's class but (X*, weak*) is not fragmentable.

引用

页码：3741 / 3747

页数：7

共 8 条

[1]

Bachman G., 1966, Functional analysis

[2]

FABIAN M, 1997, GATEAUX DIFFERENTIAB

[3] SOLUTION OF KURATOWSKI PROBLEM ON FUNCTION HAVING THE BAIRE PROPERTY .1. [J].