On some characterizations of greedy-type bases

2022/01/28 by Pablo M. Berná, Berná, Pablo M., Hùng Vidêt Chu +1
Computer Science · Engineering · Mathematics · #Advanced Optimization Algorithms Research #FOS: Mathematics #Functional Analysis (math.FA) #Optimization and Variational Analysis #Sparse and Compressive Sensing Techniques

paper · pdf · doi:10.48550/arxiv.2201.12029

openalex publication_date 2022/01/28 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28

Abstract

In 1999, S. V. Konyagin and V. N. Temlyakov introduced the so-called Thresholding Greedy Algorithm. Since then, there have been many interesting and useful characterizations of greedy-type bases in Banach spaces. In this article, we study and extend several characterizations of greedy and almost greedy bases in the literature. Along the way, we give various examples to complement our main results. Furthermore, we propose a new version of the so-called Weak Thresholding Greedy Algorithm (WTGA) and show that the convergence of this new algorithm is equivalent to the convergence of the WTGA.

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