# Performance of the Thresholding Greedy Algorithm with Larger Greedy Sums

@inproceedings{Chu2022PerformanceOT, title={Performance of the Thresholding Greedy Algorithm with Larger Greedy Sums}, author={H{\`u}ng Việt Chu}, year={2022} }

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…

## References

SHOWING 1-10 OF 21 REFERENCES

### Larger Greedy Sums for Reverse Partially Greedy Bases

- Mathematics
- 2022

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…

### On the existence of almost greedy bases in Banach spaces

- Mathematics
- 2003

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…

### Strong Partially Greedy Bases and Lebesgue-Type Inequalities

- MathematicsConstructive Approximation
- 2021

In this paper, we continue the study of Lebesgue-type inequalities for greedy algorithms. We introduce the notion of strong partially greedy Markushevich bases and study the Lebesgue-type parameters…

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

- Mathematics, EconomicsAnnals 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

- MathematicsStudia Mathematica
- 2021

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…