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    Non-superreflexivity of Garling sequence spaces and applications to the existence of special types of conditional bases

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    2020100468_Albiac_NonSuperReflexivityGarling.pdf (334.8Kb)
    Date
    2020
    Author
    Albiac Alesanco, Fernando José Upna Orcid
    Ansorena, José L. 
    Dilworth, S. J. 
    Kutzarova, Denka 
    Version
    Acceso abierto / Sarbide irekia
    Type
    Artículo / Artikulua
    Version
    Versión aceptada / Onetsi den bertsioa
    Project Identifier
    ES/1PE/MTM2016-76808-P 
    Impact
     
     
     
    10.4064/sm180910-1-2
     
     
     
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    Abstract
    We settle in the negative the problem of the superreflexivity of Garling sequence spaces by showing that they contain a complemented subspace isomorphic to a non-superreflexive mixed-norm sequence space. As a by-product, we give applications to the study of conditional Schauder bases and conditional almost greedy bases in this new class of Banach spaces. ... [++]
    We settle in the negative the problem of the superreflexivity of Garling sequence spaces by showing that they contain a complemented subspace isomorphic to a non-superreflexive mixed-norm sequence space. As a by-product, we give applications to the study of conditional Schauder bases and conditional almost greedy bases in this new class of Banach spaces. [--]
    Subject
    Subsymmetric basis, Garling sequence spaces, Superreflexivity, Besov spaces, Conditional bases, Conditionality constants, Almost greedy bases
     
    Publisher
    Instytut Matematyczny
    Published in
    Studia Mathematica, 2020, 251(3), 277-288
    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/10.4064/sm180910-1-2
    URI
    https://hdl.handle.net/2454/39431
    Sponsorship
    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 Analisis Vectorial, multilineal, y aproximacion. F. Albiac was also supported by the grant MTM2016-76808-P (MINECO, Spain) for Operators, lattices, and structure of Banach spaces. S. J. Dilworth was supported by the National Science Foundation under Grant Number DMS-1361461. Denka Kutzarova acknowledges the support from Simmons Foundation Collaborative Grant Number 636954. S. J. Dilworth and D. Kutzarova were supported by the Workshop in Analysis and Probability at Texas A&M University in 2017.
    Appears in Collections
    • Artículos de revista InaMat - InaMat aldizkari artikuluak [235]
    • Artículos de revista - Aldizkari artikuluak [4211]
    • Artículos de revista DEIM - EIMS Aldizkari artikuluak [207]
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