Publication: Greedy approximation for biorthogonal systems in quasi-Banach spaces
Date
Authors
Director
Publisher
Project identifier
ES/1PE/MTM2016-76566-P
AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PGC2018-095366-B-I00/ES/
AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2019-107701GB-I00/ES/
Abstract
The general problem addressed in this work is the development of a systematic study of the thresholding greedy algorithm for general biorthogonal systems in quasi-Banach spaces from a functional-analytic point of view. If (Formula Presented) is a biorthogonal system in X then for each x ∈ X we have a formal expansion (Formula Presented). The thresholding greedy algorithm (with threshold ε > 0) applied to x is formally defined as (Formula Presented). The properties of this operator give rise to the different classes of greedy-type bases. We revisit the concepts of greedy, quasi-greedy, and almost greedy bases in this comprehensive framework and provide the (non-trivial) extensions of the corresponding characterizations of those types of bases. As a by-product of our work, new properties arise, and the relations among them are carefully discussed.
Description
Keywords
Department
Faculty/School
Degree
Doctorate program
item.page.cita
item.page.rights
© Instytut Matematyczny PAN, Warszawa 2021.
Los documentos de Academica-e están protegidos por derechos de autor con todos los derechos reservados, a no ser que se indique lo contrario.