Banach spaces with a unique greedy basis

  1. Albiac, F. 5
  2. Ansorena, J.L. 3
  3. Dilworth, S.J. 2
  4. Kutzarova, D. 14
  1. 1 University of Illinois at Urbana Champaign
    info

    University of Illinois at Urbana Champaign

    Urbana, Estados Unidos

    ROR https://ror.org/047426m28

  2. 2 University of South Carolina
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    University of South Carolina

    Columbia, Estados Unidos

    ROR https://ror.org/02b6qw903

  3. 3 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

  4. 4 Institute of Mathematics Bulgarian Academy of Sciences, Sofia, Bulgaria
  5. 5 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: 2016

Volumen: 210

Páginas: 80-102

Tipo: Artículo

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DOI: 10.1016/J.JAT.2016.06.005 SCOPUS: 2-s2.0-84978271593 WoS: WOS:000382348600005 GOOGLE SCHOLAR

Otras publicaciones en: Journal of Approximation Theory

Resumen

The purpose of this article is to undertake an in-depth study of the properties of existence and uniqueness of greedy bases in Banach spaces. We show that greedy bases fail to exist for a range of neo-classical spaces within the family of Nakano and Orlicz sequence spaces and find the first-known cases of non-trivial spaces (i.e., different from c0, ℓ1, and ℓ2) with a unique greedy basis. The variety and nature of those examples evince that a complete classification of Banach spaces with a unique greedy basis cannot be expected. © 2016 Elsevier Inc.