Characterization of 1-almost greedy bases

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• 作者：F. Albiac ; J. L. Ansorena
• 关键词：Thresholding greedy algorithm ; Quasi ; greedy basis ; Almost greedy basis ; Unconditional basis ; Property (A)
• 刊名：Revista Matemática Complutense
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：30
• 期：1
• 页码：13-24
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics, general; Algebra; Analysis; Applications of Mathematics; Geometry; Topology;
• 出版者：Springer Milan
• ISSN：1988-2807
• 卷排序：30

文摘

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.