Weak thresholding greedy algorithms in Banach spaces

被引：8

作者：

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

Kutzarova, Denka ^{[2
]}

Schlumprecht, Th. ^{[3
]}

Wojtaszczyk, P. ^{[4
]}

机构：

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

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

[3] Texas A&M Univ, Dept Math, College Stn, TX 78712 USA

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

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2012年 / 263卷 / 12期

基金：

美国国家科学基金会;

关键词：

Greedy approximation; Banach spaces; Thresholding greedy algorithm; Weak thresholding; BASES;

D O I：

10.1016/j.jfa.2012.09.011

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider weak thresholding greedy algorithms with respect to Markushevich bases in general Banach spaces. We find sufficient conditions for the equivalence of boundedness and convergence of the approximants. We also show that if there is a weak thresholding algorithm for the system which gives the best n-term approximation up to a multiplicative constant, then the system is already "greedy". Similar results are proved for "almost greedy" and "semi-greedy" systems. (C) 2012 Elsevier Inc. All rights reserved.

引用

页码：3900 / 3921

页数：22

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