A note on 1-semi-greedy bases in p-Banach spaces with 0 < p ≤ 1

• Autorzy: Berná Pablo M. , García Andrea , González David

Identyfikatory

DOI

10.1515/dema-2024-0047

• Języki publikacji: EN

Abstrakty

EN

The purpose of this article is to discuss about the so-called semi-greedy bases in p-Banach spaces. Specifically, we will review existing results that characterize these bases in terms of almost-greedy bases, and, also, we analyze quantitatively the behavior of certain constants. As new results, by avoiding the use of certain classical results in p-convexity, we aim to quantitatively improve specific bounds for bi-monotone 1-semi-greedy bases.

Słowa kluczowe

EN

non-linear approximation; greedy algorithm; semi-greedy bases

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2024
• Tom: Vol. 57, nr 1
• Strony: art. no. 20240047
• Opis fizyczny: Bibliogr. 17 poz., rys.

Twórcy

autor

Berná Pablo M.

• Departamento de Métodos Cuantitativos, CUNEF Universidad, Madrid, 28040, Spain

autor

García Andrea

• Departamento de Métodos Cuantitativos, CUNEF Universidad, Madrid, 28040, Spain; Universidad San Pablo-CEU, CEU Universities, Madrid, 28003, Spain

autor

González David

• Universidad San Pablo-CEU, CEU Universities, Madrid, 28003, Spain

Bibliografia

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• [12] G. Garrigós, E. Hernández, and T. Oikhberg, Lebesgue-type inequalities for quasi-greedy bases, Constr. Approx. 38 (2013), no. 3, 447–470.
• [13] S. J. Dilworth, N. J. Kalton, and D. Kutzarova, On the existence of almost greedy bases in Banach spaces, Studia Math. 159 (2003), no. 1, 67–101.
• [14] P. M. Berná, Equivalence between almost-greedy and semi-greedy bases, J. Anal. Math. 470 (2019), 218–225.
• [15] M. Berasategui and S. Lassalle, Weak Greedy algorithms and the equivalence between semi-Greedy and almost Greedy Markushevich bases, J. Fourier Anal. Appl. 29 (2023), 20.
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Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2026).