Uniqueness of unconditional basis of $\ell _{p}(c_{0})$ and $\ell _{p}(\ell _{2})$, $0< p< 1$

Volume 150 / 2002

F. Albiac, C. Leránoz Studia Mathematica 150 (2002), 35-52 MSC: 46A16, 46A35, 46A40, 46A45. DOI: 10.4064/sm150-1-4

Abstract

We prove that the quasi-Banach spaces $\ell _{p}(c_{0})$ and $\ell _{p}(\ell _{2})$ ($0< p< 1$) have a unique unconditional basis up to permutation. Bourgain, Casazza, Lindenstrauss and Tzafriri have previously proved that the same is true for the respective Banach envelopes $\ell _{1}(c_{0})$ and $\ell _{1}(\ell _{2})$. They used duality techniques which are not available in the non-locally convex case.

Authors

  • F. AlbiacDepartamento de Matemática e Informática
    Universidad Pública de Navarra
    31006 Pamplona, Spain
    e-mail
  • C. LeránozDepartamento de Matemática e Informática
    Universidad Pública de Navarra
    31006 Pamplona, Spain
    e-mail

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