Embeddings and Lebesgue-Type Inequalities for the Greedy Algorithm in Banach Spaces

被引：19

作者：

Berna, Pablo M. ^{[1
]}

Blasco, Oscar ^{[2
]}

Garrigos, Gustavo ^{[3
]}

Hernandez, Eugenio ^{[1
]}

Oikhberg, Timur ^{[4
]}

机构：

[1] Univ Autonoma Madrid, Dept Matemat, E-28049 Madrid, Spain

[2] Univ Valencia, Dept Anal Matemat, Campus Burjassot, E-46100 Valencia, Spain

[3] Univ Murcia, Dept Matemat, E-30100 Murcia, Spain

[4] Univ Illinois, Dept Math, Urbana, IL 61801 USA

来源：

CONSTRUCTIVE APPROXIMATION | 2018年 / 48卷 / 03期

关键词：

Non-linear approximation; Lebesgue-type inequality; Greedy algorithm; Quasi-greedy basis; Biorthogonal system; Discrete Lorentz space; M-TERM APPROXIMATION; BIORTHOGONAL SYSTEMS; BASES;

D O I：

10.1007/s00365-018-9415-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We obtain Lebesgue-type inequalities for the greedy algorithm for arbitrary complete seminormalized biorthogonal systems in Banach spaces. The bounds are given only in terms of the upper democracy functions of the basis and its dual. We also show that these estimates are equivalent to embeddings between the given Banach space and certain discrete weighted Lorentz spaces. Finally, the asymptotic optimality of these inequalities is illustrated in various examples of not necessarily quasi-greedy bases.

引用

页码：415 / 451

页数：37

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