Albiac Alesanco, Fernando JoséAnsorena, José L.Wojtaszczyk, Przemyslaw2021-03-172021-10-0120211432-1807 (Electronic)10.1007/s00208-020-02069-3https://academica-e.unavarra.es/handle/2454/39429We construct for each 0<p≤1 an infinite collection of subspaces of ℓp that extend the example of Lindenstrauss (Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 12, 539–542, 1964) of a subspace of ℓ1 with no unconditional basis. The structure of this new class of p-Banach spaces is analyzed and some applications to the general theory of Lp-spaces for 0<p<1 are provided. The introduction of these spaces serves the purpose to develop the theory of conditional quasi-greedy bases in p-Banach spaces for p<1. Among the topics we consider are the existence of infinitely many conditional quasi-greedy bases in the spaces ℓp for p≤1 and the careful examination of the conditionality constants of the 'natural basis' of these spaces.38 p.application/pdfeng© Springer-Verlag GmbH Germany, part of Springer Nature 2020Subspaces of ℓpBanach spacesinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccess