• Corpus ID: 248496034

Performance of the Thresholding Greedy Algorithm with Larger Greedy Sums

  title={Performance of the Thresholding Greedy Algorithm with Larger Greedy Sums},
  author={H{\`u}ng Việt Chu},
  • H. Chu
  • Published 30 April 2022
  • Computer Science, Mathematics
A BSTRACT . The goal of this note is to study the performance of the Thresholding Greedy Algorithm (TGA) when we increase the size of greedy sums by a constant factor λ ≥ 1 . We introduce the so-called ( λ , partially greedy) bases. While the case λ = 1 gives strong partially greedy bases, we show that, for each λ > 1 , there exists a (Schauder) basis that is ( λ , partially greedy) but is not strong partially greedy. Furthermore, we investigate and give examples when a basis is (1) not 1… 



Larger Greedy Sums for Reverse Partially Greedy Bases

A BSTRACT . In 1999, Konyagin and Temlyakov introduced and investigated greedy, quasi-greedy, and democratic bases. In 2003, almost greedy and partially greedy bases were introduced by Dilworth et

Characterization of 1-almost greedy bases

This article closes the cycle of characterizations of greedy-like bases in the “isometric” case initiated in Albiac and Wojtaszczyk (J. Approx. Theory 138(1):65–86, 2006) with the characterization of

Greedy algorithm with gaps

  • T. Oikhberg
  • Computer Science, Mathematics
    J. Approx. Theory
  • 2018

On the existence of almost greedy bases in Banach spaces

We consider several greedy conditions for bases in Banach spaces that arise naturally in the study of the Thresholding Greedy Algorithm (TGA). In particular, we continue the study of almost greedy

Characterization of 1-quasi-greedy bases

Weight-partially greedy bases and weight-property (A)

  • D. Khurana
  • Mathematics, Economics
    Annals of Functional Analysis
  • 2019
In this paper, motivated by the notion of $w$-Property $(A)$ defined in [2], we introduce the notions of $w$-left Property $(A)$ and $w$-right Property $(A)$. We also introduce the notions of

A note on partially-greedy bases in quasi-Banach spaces

We continue with the study of greedy-type bases in quasi-Banach spaces started in [3]. In this paper, we study partially-greedy bases focusing our attention in two main results: -Characterization of