Albiac Alesanco, Fernando JoséAnsorena, José L.Berasategui, MiguelBerná, Pablo M.Lassalle, Silvia2023-04-182023-04-182023Albiac, F., Ansorena, J. L., Berasategui, M., Berná, P. M., & Lassalle, S. (2023). Bidemocratic bases and their connections with other greedy-type bases. Constructive Approximation, 57(1), 125-160. https://doi.org/10.1007/s00365-022-09607-z0176-427610.1007/s00365-022-09607-zhttps://academica-e.unavarra.es/handle/2454/45136In nonlinear greedy approximation theory, bidemocratic bases have traditionally played the role of dualizing democratic, greedy, quasi-greedy, or almost greedy bases. In this article we shift the viewpoint and study them for their own sake, just as we would with any other kind of greedy-type bases. In particular we show that bidemocratic bases need not be quasi-greedy, despite the fact that they retain a strong unconditionality flavor which brings them very close to being quasi-greedy. Our constructive approach gives that for each 1 < p < infinity the space L-p has a bidemocratic basis which is not quasi-greedy. We also present a novel method for constructing conditional quasi-greedy bases which are bidemocratic, and provide a characterization of bidemocratic bases in terms of the new concepts of truncation quasi-greediness and partially demo-cratic bases.application/pdfeng© The Author(s) 2022. This article is licensed under a Creative Commons Attribution 4.0 International License.Nonlinear approximationThresholding greedy algorithmQuasi-greedy basisDemocracyArtículo / Artikulua2023-04-18Acceso abierto / Sarbide irekiainfo:eu-repo/semantics/openAccess