Albiac Alesanco, Fernando JoséAnsorena, José L.Wojtaszczyk, Przemyslaw2022-11-302022-11-302022Albiac, F., Ansorena, J. L., & Wojtaszczyk, P. (2022). Uniqueness of unconditional basis of H p (T) ⊕ ℓ 2 and H p ⊕(T) T for(2) 0 < p < 1. Journal of Functional Analysis, 283(7), 109597.0022-123610.1016/j.jfa.2022.109597https://academica-e.unavarra.es/handle/2454/44396Our goal in this paper is to advance the state of the art of the topic of uniqueness of unconditional basis. To that end we establish general conditions on a pair (X, Y) formed by a quasi-Banach space X and a Banach space Y which guarantee that every unconditional basis of their direct sum X ⊕ Y splits into unconditional bases of each summand. As application of our methods we obtain that, among others, the spaces Hp(Td) ⊕ T (2) and Hp(Td) ⊕ 2, for p ∈ (0, 1) and d ∈ N, have a unique unconditional basis (up to equivalence and permutation).application/pdfeng© 2022 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND licenseHardy spacesLattice techniques in quasi-Banach spacesTsirelson spaceUniqueness of unconditional basisArtículo / Artikulua2022-11-18Acceso abierto / Sarbide irekiainfo:eu-repo/semantics/openAccess