Democracy of quasi-greedy bases in -Banach spaces with applications to the efficiency of the Thresholding Greedy Algorithm in the Hardy spaces

We use new methods, specific for non-locally convex quasi-Banach spaces, to investigate when the quasi-greedy bases of a $p$ -Banach space for $0< p<1$ are democratic. The novel techniques we obtain permit to show in particular that all quasi-greedy bases of the Hardy space $H_p({\mathbb {D}})...

Full description

Saved in:
Bibliographic Details
Published in:Proceedings of the Royal Society of Edinburgh. Section A. Mathematics Vol. 154; no. 3; pp. 906 - 928
Main Authors: Albiac, Fernando, Ansorena, José L., Bello, Glenier
Format: Journal Article
Language:English
Published: Cambridge Cambridge University Press 01.06.2024
Subjects:
Algorithms
Approximation
Banach spaces
Democracy
Efficiency
Functional analysis
Geometry
Greedy algorithms
ISSN:0308-2105, 1473-7124
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We use new methods, specific for non-locally convex quasi-Banach spaces, to investigate when the quasi-greedy bases of a $p$ -Banach space for $0< p<1$ are democratic. The novel techniques we obtain permit to show in particular that all quasi-greedy bases of the Hardy space $H_p({\mathbb {D}})$ for $0< p<1$ are democratic while, in contrast, no quasi-greedy basis of $H_p({\mathbb {D}}^d)$ for $d\ge 2$ is, solving thus a problem that was raised in [7]. Applications of our results to other spaces of interest both in functional analysis and approximation theory are also provided.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0308-2105
1473-7124
DOI:10.1017/prm.2023.42