Characterization of 1-almost greedy bases

被引:0
|
作者
F. Albiac
J. L. Ansorena
机构
[1] Universidad Pública de Navarra,Mathematics Department
[2] Universidad de La Rioja,Department of Mathematics and Computer Sciences
来源
Revista Matemática Complutense | 2017年 / 30卷
关键词
Thresholding greedy algorithm; Quasi-greedy basis; Almost greedy basis; Unconditional basis; Property (A); 46B15; 41A65; 46B15;
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学科分类号
摘要
This article closes the cycle of characterizations of greedy-like bases in the “isometric” case initiated in Albiac and Wojtaszczyk (J. Approx. Theory 138(1):65–86, 2006) with the characterization of 1-greedy bases and continued in Albiac and Ansorena (J. Approx. Theory 201:7–12, 2016) with the characterization of 1-quasi-greedy bases. Here we settle the problem of providing a characterization of 1-almost greedy bases in Banach spaces. We show that a basis in a Banach space is almost greedy with almost greedy constant equal to 1 if and only if it has Property (A). This fact permits now to state that a basis is 1-greedy if and only if it is 1-almost greedy and 1-quasi-greedy. As a by-product of our work we also provide a tight estimate of the almost greedy constant of a basis in the non-isometric case.
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页码:13 / 24
页数:11
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