Concerning the Bourgain `1 Index of a Banach Space

@inproceedings{Odell2001ConcerningTB,
  title={Concerning the Bourgain `1 Index of a Banach Space},
  author={Edward Odell},
  year={2001}
}
A well known argument of James yields that if a Banach space X contains `1 ’s uniformly, then X contains `1 ’s almost isometrically. In the first half of the paper we extend this idea to the ordinal `1-indices of Bourgain. In the second half we use our results to calculate the `1-index of certain Banach spaces. Furthermore we show that the `1-index of a separable Banach space not containing `1 must be of the form ω α for some countable ordinal α. 

From This Paper

Topics from this paper.

References

Publications referenced by this paper.
Showing 1-10 of 19 references

The distortion problem

  • E. OS ODELL, SCHLUMPRECHT, TH
  • Acta Math.,
  • 1994

Averaging weakly null sequences

  • D. AO ALSPACH, E. ODELL
  • LNM 1332,
  • 1988

Baire - 1 functions and spreading models of ` 1 . Preprint . [ L ] LEMBERG , H . , Nouvelle démonstration d ’ un theorem de J . L . Krivine sur la finie representation de ` p dans un espace de Banach

  • P. KIRIAKOULI, S. NERGREPONTIS
  • Israel Journal of Mathematics
  • 1981

Nouvelle démonstration d’un theorem de J. L

  • H. LEMBERG
  • Krivine sur la finie representation de `p dans un…
  • 1981

On convergent sequences of continuous functions

  • B. BOURGAIN
  • Bull. Soc. Math. Bel.,
  • 1980

Krivine concerning block finite representability of ` p in general Banach spaces

  • L. J.
  • Journal of Functional Analysis
  • 1978

On a theorem of J. L. Krivine concerning block finite representability of `p in general Banach spaces

  • H. ROSENTHAL
  • Journal of Functional Analysis,
  • 1978

Les derivations en theorie descriptive des ensembles et le theoreme de la borne

  • C. DELLACHERIE
  • LNM 581,
  • 1977

Similar Papers

Loading similar papers…