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Uniqueness of unconditional bases in nonlocally convex c0-products

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Abstract

We show that the c 0-product (X ⊕ X ⊕ ... ⊕ X ⊕ ...)0 of a natural quasi-Banach space X with strongly absolute unconditional basis has a unique unconditional basis up to permutation. Our results apply to a wide range of cases, including most of the c 0-products of the nonlocally convex classical quasi-Banach spaces.

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Authors and Affiliations

  1. Departamento de Matemáticas, Universidad Pública de Navarra, Pamplona, 31006, Spain

    F. Albiac & C. Leránoz

Authors
  1. F. Albiac
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  2. C. Leránoz
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Correspondence to F. Albiac.

Additional information

We would like to dedicate this paper to the memory of Professor Nigel Kalton.

The authors acknowledge support from the Spanish Research Grant Estructuras y Complejidad en Espacios de Banach II, reference number MTM2010-20190-C02-02.

The first-named author was supported by the Spanish Research Grant Operadores, reticulos, y geometria de espacios de Banach, reference number MTM2008-02652/MTM.

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Albiac, F., Leránoz, C. Uniqueness of unconditional bases in nonlocally convex c0-products. Isr. J. Math. 184, 79–91 (2011). https://doi.org/10.1007/s11856-011-0060-2

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  • DOI: https://doi.org/10.1007/s11856-011-0060-2

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