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    On certain subspaces of p for 0 < p ≤ 1 and their applications to conditional quasi-greedy bases in p-Banach spaces

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    2020100261_Albiac_OnCertainSubspaces.pdf (357.0Kb)
    Date
    2021
    Author
    Albiac Alesanco, Fernando José Upna Orcid
    Ansorena, José L. 
    Wojtaszczyk, Przemyslaw 
    Version
    Acceso abierto / Sarbide irekia
    Type
    Artículo / Artikulua
    Version
    Versión aceptada / Onetsi den bertsioa
    Project Identifier
    ES/1PE/MTM2016-76808-P 
    Impact
     
     
     
    10.1007/s00208-020-02069-3
     
     
     
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    Abstract
    We 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 ... [++]
    We 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. [--]
    Subject
    Subspaces of ℓp, Banach spaces
     
    Publisher
    Springer
    Published in
    Mathematische Annalen, 2021, 379, 465–502
    Departament
    Universidad Pública de Navarra. Departamento de Estadística, Informática y Matemáticas / Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa. InaMat - Institute for Advanced Materials / Nafarroako Unibertsitate Publikoa. Estatistika, Informatika eta Matematika Saila
     
    Publisher version
    https://doi.org/10.1007/s00208-020-02069-3
    URI
    https://hdl.handle.net/2454/39429
    Sponsorship
    F. Albiac acknowledges the support of the Spanish Ministry for Economy and Competitivity under Grant MTM2016-76808-P as well as the Spanish Ministry for Science and Innovation under Grant PID2019-1077701GB-I00 for Operators, lattices, and structure of Banach spaces. F. Albiac and J. L. Ansorena acknowledge the support of the Spanish Ministry for Science, Innovation, and Universities under Grant PGC2018-095366-B-I00 for Análisis Vectorial, Multilineal y Aproximación. P. Wojtaszczyk was supported by National Science Centre, Poland Grant UMO-2016/21/B/ST1/00241.
    Appears in Collections
    • Artículos de revista InaMat - InaMat aldizkari artikuluak [235]
    • Artículos de revista - Aldizkari artikuluak [4210]
    • Artículos de revista DEIM - EIMS Aldizkari artikuluak [207]
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