Albiac Alesanco, Fernando JoséAnsorena, José L.Bello, GlenierWojtaszczyk, Przemyslaw2023-10-302023-10-302023Albiac, F., Ansorena, J. L., Bello, G., & Wojtaszczyk, P. (2023). Existence of almost greedy bases in mixed-norm sequence and matrix spaces, including besov spaces. Constructive Approximation. https://doi.org/10.1007/s00365-023-09662-00176-427610.1007/s00365-023-09662-0https://academica-e.unavarra.es/handle/2454/46667We prove that the sequence spaces lp ⊕ lq and the spaces of infinite matrices lp(lq ), lq l(p) and ( ∞ n=1 n lp)lq , which are isomorphic to certain Besov spaces, have an almost greedy basis whenever 0 < p < 1 < q < ∞. More precisely, we custom-build almost greedy bases in such a way that the Lebesgue parameters grow in a prescribed manner. Our arguments critically depend on the extension of the Dilworth–Kalton– Kutzarova method from Dilworth et al. (Stud Math 159(1):67–101, 2003), which was originally designed for constructing almost greedy bases in Banach spaces, to make it valid for direct sums of mixed-normed spaces with nonlocally convex components. Additionally, we prove that the fundamental functions of all almost greedy bases of these spaces grow as (ml/q )∞ m=l.application/pdfeng© 2023, The Author(s). This article is licensed under a CreativeCommonsAttribution 4.0 InternationalLicense.Almost greedy basisConditional basisQuasi-greedy basisSubsymmetric basisThresholding greedy algorithmlp-SpacesArtículo / Artikulua2023-10-30Acceso abierto / Sarbide irekiainfo:eu-repo/semantics/openAccess