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...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Journal of approximation theory Jg. 201; S. 7 - 12
Hauptverfasser: Albiac, F., Ansorena, J.L.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier Inc 01.01.2016
Schlagworte:
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-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung: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