Positivity

, Volume 8, Issue 4, pp 443–454 | Cite as

Uniqueness of the Unconditional Basis of ℓ1 (ℓ p ) and ℓ p (ℓ1), 0 < p < 1

Article
Accepted:

Abstract

We prove that the quasi-Banach spaces ℓ1 (ℓ p ) and ℓ p (ℓ1), 0 < p < 1 have a unique unconditional basis up to permutation

Keywords

Fourier Analysis Operator Theory Potential Theory Unconditional Basis Unique Unconditional Basis 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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References

  1. 1.
    Albiac, F., Leránoz, C. 2002Uniqueness of unconditional basis of ℓ p (c0) and ℓ p (ℓ2), 0 < p < 1Studia Math.1503551Google Scholar
  2. 2.
    Bollobas, B. 1986CombinatoricsCambridge University PressCambridgeGoogle Scholar
  3. 3.
    Bourgain J., Casazza P.G., Lindenstrauss J., Tzafriri L. (1985). Banach spaces with a unique unconditional basis, up to permutation, Mem. Amer. Math. Soc. 322: Providence, 1985Google Scholar
  4. 4.
    Casazza, P.G., Kalton, N.J. 1998Uniqueness of unconditional bases in Banach spacesIsrael J Math.103141176Google Scholar
  5. 5.
    Edelstein, I.S., Wojtaszczyk, P. 1976On projections and unconditional bases in direct sums of Banach spacesStudia Math.56263276Google Scholar
  6. 6.
    Kalton, N.J. 1977Orlicz sequence spaces without local convexityMath. Proc. Camb. Phil. Soc.81253278Google Scholar
  7. 7.
    Kalton, N.J. 1984Convexity conditions on non-locally convex latticesGlasgow Math. J.25141152Google Scholar
  8. 8.
    Kalton, N.J., Peck, N.T., Roberts, J.W. 1985An F-space Sampler, London Math Soc. Lecture Note Ser. 89Cambridge University PressCambridgeGoogle Scholar
  9. 9.
    Kalton, N.J. 1986Banach envelopes of non-locally convex spacesCanad. J. Math.386586Google Scholar
  10. 10.
    Kalton, N.J., Leránoz, C., Wojtaszczyk, P. 1990Uniqueness of unconditional bases in quasi- Banach spaces with applications to Hardy spacesIsrael J. Math.72299311Google Scholar
  11. 11.
    Leránoz, C. 1992Uniqueness of unconditional basis of c0 (ℓ p ), 0 < p < 1Studia Math.102193207Google Scholar
  12. 12.
    Lindenstrauss, J., Pelczynski, A. 1968Absolutely summing operators in L p -spaces and their applicationsStudia Math.29275326Google Scholar
  13. 13.
    Lindenstrauss, J., Tzafriri, L. 1979Classical Banach Spaces II, Function spacesSpringer VerlagBerlin, Heidelberg, New YorkGoogle Scholar
  14. 14.
    Lindenstrauss, J., Zippin, M. 1969Banach spaces with a unique unconditional basisJFunctional Analysis.3115125Google Scholar
  15. 15.
    Mityagin, B.S. 1970Equivalence of bases in Hilbert scalesStudia Math.37111137(inRussian)Google Scholar
  16. 16.
    Wojtaszczyk, P. 1997Uniqueness of unconditional bases in quasi-Banach spaces with applications to Hardy spaces, IIIsrael J. Math.97253280Google Scholar
  17. 17.
    Wojtowicz, M. 1988On Cantor-Bernstein type theorems in Riesz spacesIndag. Math.9193100Google Scholar

Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Missouri-ColumbiaColumbiaUSA
  2. 2.Departamento de Matemática e InformáticaUniversidad Publica de NavarraPamplonaSpain

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