Characterization of 1-quasi-greedy bases

JOURNAL OF APPROXIMATION THEORY

卷:201

Article

Albiac, F.¹  Ansorena, J. L.² 

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

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

关键词: Thresholding greedy algorithm;    Quasi-greedy basis;    Unconditional basis;    Renorming;   

DOI  :  10.1016/j.jat.2015.08.006

来源: Elsevier

【 摘 要 】

In this note we continue the study initiated in Albiac and Wojtaszczyk (2006) of greedy-like bases in the isometric case, i.e., in the case that the constants that arise in the context of greedy bases in their different forms are 1. Here we settle the problem to find a satisfactory characterization of 1-quasi-greedy bases in Banach spaces. We show that a semi-normalized basis in a Banach space is quasi-greedy with quasi-greedy constant 1 if and only if it is unconditional with suppression-unconditional constant 1. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

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