Banach spaces with a unique greedy basis

被引：9

作者：

Albiac, F. ^{[1
]}

Ansorena, J. L. ^{[2
]}

Dilworth, S. J. ^{[3
]}

Kutzarova, Denka ^{[4
,5
]}

机构：

[1] Univ Publ Navarra, Dept Math, Pamplona 31006, Spain

[2] Univ La Rioja, Dept Math & Comp Sci, Logrono 26004, Spain

[3] Univ South Carolina, Dept Math, Columbia, SC 29208 USA

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

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

来源：

JOURNAL OF APPROXIMATION THEORY | 2016年 / 210卷

基金：

美国国家科学基金会;

关键词：

Greedy basis; Unconditional basis; Symmetric basis; Marcinkiewicz spaces; Nakano spaces; Orlicz sequence spaces; Uniqueness greedy (respectively; unconditional or symmetric) basis; UNCONDITIONAL BASES;

D O I：

10.1016/j.jat.2016.06.005

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The purpose of this article is to undertake an in-depth study of the properties of existence and uniqueness of greedy bases in Banach spaces. We show that greedy bases fail to exist for a range of neo-classical spaces within the family of Nakano and Orlicz sequence spaces and find the first-known cases of non-trivial spaces (i.e., different from c(0), l(1), and l(2)) with a unique greedy basis. The variety and nature of those examples evince that a complete classification of Banach spaces with a unique greedy basis cannot be expected. (C) 2016 Elsevier Inc. All rights reserved.

引用

页码：80 / 102

页数：23

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