Albiac Alesanco, Fernando José

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https://academica-e.unavarra.es/handle/2454/48472

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Albiac Alesanco

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Fernando José

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Estadística, Informática y Matemáticas

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InaMat2. Instituto de Investigación en Materiales Avanzados y Matemáticas

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0000-0001-7051-9279

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88452

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504

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2019 - 201912020 - 20231
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Author: Wojtaszczyk, Przemyslaw × Subject: Conditional basis ×

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Now showing 1 - 2 of 2
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    PublicationOpen Access
    Conditional quasi-greedy bases in non-superreflexive Banach spaces
    (Springer, 2019) Albiac Alesanco, Fernando José; Ansorena, José L.; Wojtaszczyk, Przemyslaw; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
    For a conditional quasi-greedy basis B in a Banach space, the associated conditionality constants km[B] verify the estimate km[B]=O(logm). Answering a question raised by Temlyakov, Yang, and Ye, several authors have studied whether this bound can be improved when we consider quasi-greedy bases in some special class of spaces. It is known that every quasi-greedy basis in a superreflexive Banach space verifies km[B]=O((logm)1-E) for some 0
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    PublicationOpen Access
    Existence of almost greedy bases in mixed-norm sequence and matrix spaces, including besov spaces
    (Springer, 2023) Albiac Alesanco, Fernando José; Ansorena, José L.; Bello, Glenier; Wojtaszczyk, Przemyslaw; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute for Advanced Materials and Mathematics - INAMAT2; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa
    We 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.