1-greedy renormings of Garling sequence spaces

  1. Albiac, F. 3
  2. Ansorena, J.L. 2
  3. Wallis, B. 1
  1. 1 Northern Illinois University
    info

    Northern Illinois University

    DeKalb, Estados Unidos

    ROR https://ror.org/012wxa772

  2. 2 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

  3. 3 Universidad Pública de Navarra
    info

    Universidad Pública de Navarra

    Pamplona, España

    ROR https://ror.org/02z0cah89

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Revista:
Journal of Approximation Theory

ISSN: 0021-9045

Año de publicación: 2018

Volumen: 230

Páginas: 13-23

Tipo: Artículo

DOI: 10.1016/J.JAT.2018.03.002 SCOPUS: 2-s2.0-85044568572 GOOGLE SCHOLAR

Otras publicaciones en: Journal of Approximation Theory

Resumen

We show that all Garling sequence spaces admit a renorming with respect to which their standard unit vector basis is 1-greedy. We also discuss some additional properties of these Banach spaces related to uniform convexity and superreflexivity. In particular, our approach to the study of the superreflexivity of Garling sequence spaces provides an example of how essentially non-linear tools from greedy approximation can be used to shed light on the linear structure of these spaces. © 2018 Elsevier Inc.