Szlenk and w*-dentability indices of the Banach spaces C([0, α])

被引：6
|
作者：
Brooker, Philip A. H. [1 ]
机构：
[1] Australian Natl Univ, Inst Math Sci, Canberra, ACT 0200, Australia
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2013年 / 399卷 / 02期
关键词：
Szlenk index; Dentability index; WEAK-ASTERISK; QUOTIENTS;
D O I：
10.1016/j.jmaa.2012.10.028
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let a be an infinite ordinal and gamma the unique ordinal satisfying omega(omega gamma) <= alpha < omega(omega gamma+1). We show that the Banach space C([0, alpha]) of all continuous scalar-valued functions on the compact ordinal interval [0, alpha] has Szlenk index equal to omega(gamma+1) and w*-dentability index equal to omega(1+gamma+1). (C) 2012 Elsevier Inc. All rights reserved.
引用
收藏
页码：559 / 564
页数：6
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