Albiac Alesanco, Fernando JoséAnsorena, José L.Wojtaszczyk, Przemyslaw2021-09-062023-04-0120200022-123610.1016/j.jfa.2020.108871https://academica-e.unavarra.es/handle/2454/40416The list of known Banach spaces whose linear geometry determines the (nonlinear) democracy functions of their quasi-greedy bases to the extent that they end up being democratic, reduces to c0, ℓ2, and all separable L1-spaces. Oddly enough, these are the only Banach spaces that, when they have an unconditional basis, it is unique. Our aim in this paper is to study the connection between quasi-greediness and democracy of bases in non-locally convex spaces. We prove that all quasi-greedy bases in ℓp for 0<p<1 (which also has a unique unconditional basis) are democratic with fundamental function of the same order as (m1/p)∞m=1. The methods we develop allow us to obtain even more, namely that the same occurs in any separable Lp-space, 0<p<1, with the bounded approximation property.22 p.application/pdfeng© 2020 Elsevier Inc. This manuscript version is made available under the CC-BY-NC-ND 4.0Democratic basisQuasi-Banach spacesQuasi-greedy basisSequence spacesinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccess