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

被引：8

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
Albiac, F
Wojtaszczyk, P
[J]. JOURNAL OF APPROXIMATION THEORY, 2006, 138 (01) : 65 - 86
[2] Albiac F., DISSERTATIONES MATH
[3] 1-greedy renormings of Garling sequence spaces
Albiac, Fernando
Ansorena, Jose L.
Wallis, Ben
[J]. JOURNAL OF APPROXIMATION THEORY, 2018, 230 : 13 - 23
[4] [Anonymous], 1957, Bull. Acad. Polon. Sci. Cl.
[5] [Anonymous], 1942, Proc. Imp. Acad. Tokyo
[6] Berasategui M., CONSTR APPROX
[7] Characterization of greedy bases in Banach spaces
Berna, Pablo M.
Blasco, Oscar
[J]. JOURNAL OF APPROXIMATION THEORY, 2017, 215 : 28 - 39
[8] Renorming spaces with greedy bases
Dilworth, S. J.
Kutzarova, D.
Odell, E.
Schlumprecht, Th.
Zsak, A.
[J]. JOURNAL OF APPROXIMATION THEORY, 2014, 188 : 39 - 56
[9] On the existence of almost greedy bases in Banach spaces
Dilworth, SJ
Kalton, NJ
Kutzarova, D
[J]. STUDIA MATHEMATICA, 2003, 159 (01) : 67 - 101
[10] The thresholding greedy algorithm, greedy bases, and duality
Dilworth, SJ
Kalton, NJ
Kutzarova, D
Temlyakov, VN
[J]. CONSTRUCTIVE APPROXIMATION, 2003, 19 (04) : 575 - 597

← 1 2 →