Albiac Alesanco, Fernando JoséAnsorena, José L.Berná, Pablo M.Wojtaszczyk, Przemyslaw2022-01-262022-04-2920210012-386210.4064/dm817-11-2020https://academica-e.unavarra.es/handle/2454/41955The 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.104 p.application/pdfeng© Instytut Matematyczny PAN, Warszawa 2021.Almost greedyDemocratic basisGreedy basisQuasi-Banach spacesQuasi-greedy basisUnconditional basisinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccessAcceso abierto / Sarbide irekia