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
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    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 the London Mathematical Society Print

ISSN: 0024-6107

Año de publicación: 2018

Tipo: Artículo

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DOI: 10.1112/JLMS.12129 SCOPUS: 2-s2.0-85044594300 GOOGLE SCHOLAR

Otras publicaciones en: Journal of the London Mathematical Society Print

Repositorio institucional: lock_openAcceso abierto Editor

Resumen

The aim of this paper is to introduce and investigate a new class of separable Banach spaces modeled after an example of Garling from 1968. For each 1≤p<∞ and each nonincreasing weight w∈c0(set minus)ℓ1, we exhibit an ℓp-saturated, complementably homogeneous, and uniformly subprojective Banach space g(w,p). We also show that g(w,p) admits a unique subsymmetric basis despite the fact that for a wide class of weights it does not admit a symmetric basis. This provides the first known examples of Banach spaces where those two properties coexist. © 2018 London Mathematical Society.