The Szlenk index of Lp(X)

被引：4
|
作者：
Hajek, Petr [1 ,2 ]
Schlumprecht, Thomas [2 ,3 ]
机构：
[1] Acad Sci Czech Republic, Math Inst, CR-11567 Prague 1, Czech Republic
[2] Czech Tech Univ, Fac Elect Engn, Dept Math, Prague 16000, Czech Republic
[3] Texas A&M Univ, Dept Math, College Stn, TX 77843 USA
来源：
BULLETIN OF THE LONDON MATHEMATICAL SOCIETY | 2014年 / 46卷
基金：
美国国家科学基金会;
关键词：
SEPARABLE BANACH-SPACES; DENTABILITY INDEX; WEAK-ASTERISK;
D O I：
10.1112/blms/bdt106
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We find an optimal upper bound on the values of the weak*-dentability index Dz(X) in terms of the Szlenk index Sz(X) of a Banach space X with separable dual. Namely, if Sz(X) =omega(alpha), for some alpha < omega(1), and p epsilon (1,infinity), then Sz(X) <= Dz(X) <= Sz(L-p(X)) <= {omega(alpha+1) if alpha is a finite ordinal, omega(alpha) if alpha is an infinite ordinal.
引用
收藏
页码：415 / 424
页数：10
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