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

页码：415 / 424

页数：10

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