Weak Convergence of Greedy Algorithms in Banach Spaces

被引：7

作者：

Dilworth, S. J. ^{[1
]}

Kutzarova, Denka ^{[2
]}

Shuman, Karen L. ^{[3
]}

Temlyakov, V. N. ^{[1
]}

Wojtaszczyk, P. ^{[4
]}

机构：

[1] Univ S Carolina, Dept Math, Columbia, SC 29208 USA

[2] Bulgarian Acad Sci, Inst Math, Sofia, Bulgaria

[3] Grinnell Coll, Dept Math, Grinnell, IA 50112 USA

[4] Warsaw Univ, Inst Appl Math, PL-02097 Warsaw, Poland

来源：

JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS | 2008年 / 14卷 / 5-6期

关键词：

Greedy algorithms; Weak convergence; Uniformly smooth Banach spaces; Uniform Opial property;

D O I：

10.1007/s00041-008-9034-0

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the convergence of certain greedy algorithms in Banach spaces. We introduce the WN property for Banach spaces and prove that the algorithms converge in the weak topology for general dictionaries in uniformly smooth Banach spaces with the WN property. We show that reflexive spaces with the uniform Opial property have theWN property. We show that our results do not extend to algorithms which employ a 'dictionary dual' greedy step.

引用

页码：609 / 628

页数：20

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