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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Bibliographic Details
Published in:	Journal of approximation theory Vol. 201; pp. 7 - 12
Main Authors:	Albiac, F., Ansorena, J.L.
Format:	Journal Article
Language:	English
Published:	Elsevier Inc 01.01.2016
Subjects:	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
Online Access:	Get full text
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Summary:	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