A note on partially-greedy bases in quasi-Banach spaces

被引：9

作者：

Berna, Pablo M. ^{[1
]}

机构：

[1] Univ San Pablo CEU, CEU Univ, Fac Ciencias Econ & Empresariales, Dept Matemat Aplicada & Estadist, Madrid 28003, Spain

来源：

STUDIA MATHEMATICA | 2021年 / 259卷 / 02期

关键词：

quasi-Banach spaces; greedy bases; quasi-greedy bases; greedy algorithm; ALGORITHM;

D O I：

10.4064/sm200402-20-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We continue the study of greedy-type bases in quasi-Banach spaces started by Albiac et al. [arXiv:1903.11651]. In the present paper, we study partially-greedy bases, focusing on two main results: Characterization of partially-greedy bases in quasi-Banach spaces in terms of quasi-greediness and various conservative-like properties. Given a C-partially-greedy basis in a quasi-Banach space, there exists a "renorming" such that the basis is 1-partially-greedy.

引用

页码：225 / 239

页数：15

共 12 条

[1] Characterization of 1-greedy bases [J].

Albiac, F ;

Wojtaszczyk, P .

JOURNAL OF APPROXIMATION THEORY, 2006, 138 (01) :65-86

[2]

Albiac F., DISSERTATIONES MATH

[3] 1-greedy renormings of Garling sequence spaces [J].

Albiac, Fernando ;

Ansorena, Jose L. ;

Wallis, Ben .

JOURNAL OF APPROXIMATION THEORY, 2018, 230 :13-23

[4]

Aoki T., 1942, Proc. Imp. Acad. Tokyo, V18, P588

[5]

Berasategui M., CONSTR APPROX

[6] Characterization of greedy bases in Banach spaces [J].

Berna, Pablo M. ;

Blasco, Oscar .

JOURNAL OF APPROXIMATION THEORY, 2017, 215 :28-39

[7] Renorming spaces with greedy bases [J].

Dilworth, S. J. ;

Kutzarova, D. ;

Odell, E. ;

Schlumprecht, Th. ;

Zsak, A. .

JOURNAL OF APPROXIMATION THEORY, 2014, 188 :39-56

[8] On the existence of almost greedy bases in Banach spaces [J].

Dilworth, SJ ;

Kalton, NJ ;

Kutzarova, D .

STUDIA MATHEMATICA, 2003, 159 (01) :67-101

[9] The thresholding greedy algorithm, greedy bases, and duality [J].

Dilworth, SJ ;

Kalton, NJ ;

Kutzarova, D ;

Temlyakov, VN .

CONSTRUCTIVE APPROXIMATION, 2003, 19 (04) :575-597

[10]

Konyagin S.V., 1999, East J. Approx., V5, P365

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