Characterization of 1-quasi-greedy bases

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 characterizatio...

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Vydáno v:Journal of approximation theory Ročník 201; s. 7 - 12
Hlavní autoři: Albiac, F., Ansorena, J.L.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier Inc 01.01.2016
Témata:
Quasi-greedy basis
Renorming
Thresholding greedy algorithm
Unconditional basis
Renorming
Quasi-greedy basis
46B15
Thresholding greedy algorithm
Unconditional basis
41A65
ISSN:0021-9045, 1096-0430
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Popis
Shrnutí: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.
ISSN:0021-9045
1096-0430
DOI:10.1016/j.jat.2015.08.006