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A new approach to the Ramsey-type games and the Gowers dichotomy in F-spaces

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Abstract

We give a new approach to the Ramsey-type results of Gowers on block bases in Banach spaces and apply our results to prove the Gowers dichotomy in F-spaces.

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References

  1. J. Bagaria and J. López-Abad: Weakly Ramsey sets in Banach spaces, Adv. Math.160 (2001), 133–174.

    Article  MATH  MathSciNet  Google Scholar 

  2. J. Bagaria and J. López-Abad: Determinacy and weakly Ramsey sets in Banach spaces, Trans. Amer. Math. Soc.354 (2002), 1327–1349 (electronic).

    Article  MATH  MathSciNet  Google Scholar 

  3. T. Figiel, R. Frankiewicz, R. Komorowski and C. Ryll-Nardzewski: On hereditarily indecomposable Banach spaces, Ann. Pure Appl. Logic126 (2004), 293–299.

    Article  MATH  MathSciNet  Google Scholar 

  4. W. T. Gowers: A new dichotomy for Banach spaces, Geom. Funct. Anal.6 (1996), 1083–1093.

    Article  MATH  MathSciNet  Google Scholar 

  5. W. T. Gowers: An infinite Ramsey theorem and some Banach-space dichotomies, Ann. of Math. (2)156 (2002), 797–833.

    Article  MATH  MathSciNet  Google Scholar 

  6. W. T. Gowers: Ramsey methods in Banach spaces, in: Handbook of the geometry of Banach spaces, Vol. 2, (2003), pp. 1071–1097, North-Holland, Amsterdam.

    Article  MathSciNet  Google Scholar 

  7. W. T. Gowers and B. Maurey: The unconditional basic sequence problem, J. Amer. Math. Soc.6 (1993), 851–874.

    MATH  MathSciNet  Google Scholar 

  8. N. J. Kalton: Basic sequences in F-spaces and their applications, Proc. Edinburgh Math. Soc. (2)19 (1974/75), 151–167.

    Article  MATH  MathSciNet  Google Scholar 

  9. N. J. Kalton: An elementary example of a Banach space not isomorphic to its complex conjugate, Canad. Math. Bull.38 (1995), 218–222.

    MATH  MathSciNet  Google Scholar 

  10. N. J. Kalton: The basic sequence problem, Studia Math.116 (1995), 167–187.

    MATH  MathSciNet  Google Scholar 

  11. N. J. Kalton, N. T. Peck and J. W. Roberts: An F-space sampler, London Mathematical Society Lecture Note Series, 89, Cambridge University Press, Cambridge, 1984.

    MATH  Google Scholar 

  12. N. J. Kalton and J. H. Shapiro: Bases and basic sequences in F-spaces, Studia Math.56 (1976), 47–61.

    MATH  MathSciNet  Google Scholar 

  13. B. Maurey: A note on Gowers’ dichotomy theorem, in: Convex geometric analysis, Berkeley, CA, 1996; Math. Sci. Res. Inst. Publ., 34, (1999), pp. 149–157, Cambridge Univ. Press, Cambridge.

  14. A. M. Pelczar: Some version of Gowers’ dichotomy for Banach spaces, Univ. Iagel. Acta Math.41 (2003), 235–243.

    MathSciNet  Google Scholar 

  15. M. L. Reese: Almost-atomic spaces, Illinois J. Math.36 (1992), 316–324.

    MATH  MathSciNet  Google Scholar 

  16. W. Żelazko: On the radicals of p-normed algebras, Studia Math.21 (1961/1962), 203–206.

    MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, University of South Carolina, Columbia, SC, 29208, USA

    George Androulakis & Stephen J. Dilworth

  2. Department of Mathematics, University of Missouri-Columbia, Columbia, MO, 65211, USA

    Nigel J. Kalton

Authors
  1. George Androulakis
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  2. Stephen J. Dilworth
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  3. Nigel J. Kalton
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Corresponding author

Correspondence to George Androulakis.

Additional information

The second author was supported by NSF grant DMS-0701552.

The third author was supported by NSF grant DMS-0555670.

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Androulakis, G., Dilworth, S.J. & Kalton, N.J. A new approach to the Ramsey-type games and the Gowers dichotomy in F-spaces. Combinatorica 30, 359–385 (2010). https://doi.org/10.1007/s00493-010-2507-1

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