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Conditionality constants of quasi-greedy bases in super-reflexive Banach spaces

Volume 227 / 2015

F. Albiac, J. L. Ansorena, G. Garrigós, E. Hernández, M. Raja Studia Mathematica 227 (2015), 133-140 MSC: Primary 41A65; Secondary 41A46, 46B15. DOI: 10.4064/sm227-2-3

Abstract

We show that in a super-reflexive Banach space, the conditionality constants $k_N(\mathscr B)$ of a quasi-greedy basis $\mathscr B$ grow at most like $O((\log N)^{1-\varepsilon})$ for some $0 < \varepsilon < 1$. This extends results by the third-named author and Wojtaszczyk (2014), where this property was shown for quasi-greedy bases in $L_p$ for $1< p< \infty$. We also give an example of a quasi-greedy basis $\mathscr B$ in a reflexive Banach space with $k_N(\mathscr B)\approx \log N$.

Authors

  • F. AlbiacDepartamento de Matemáticas
    Universidad Pública de Navarra
    31006 Pamplona, Spain
    e-mail
  • J. L. AnsorenaDepartmento de Matemáticas y Computaci\xF3n
    Universidad de La Rioja
    26004 Logrońo, Spain
    e-mail
  • G. GarrigósDepartamento de Matemáticas
    Universidad de Murcia
    30100 Murcia, Spain
    e-mail
  • E. HernándezDepartamento de Matemáticas
    Universidad Autónoma de Madrid
    28049 Madrid, Spain
    e-mail
  • M. RajaDepartamento de Matemáticas
    Universidad de Murcia
    30100 Murcia, Spain
    e-mail

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