ON THE SZLENK INDEX AND THE WEAK*- DENTABILITY INDEX

@inproceedings{Lancien1996ONTS,
  title={ON THE SZLENK INDEX AND THE WEAK*- DENTABILITY INDEX},
  author={Gilles Lancien},
  year={1996}
}
  • Gilles Lancien
  • Published 1996
  • Mathematics
  • We prove that if the Szlenk index Sz(X) and the weak*-dentability index δ∗(X) of a Banach space X are countable, then they are determined by the closed separable linear subspaces of X. From this we deduce the existence of an absolute function ψ from ω1 to ω1 (first uncountable ordinal) such that δ∗(X) is bounded above by ψ(Sz(X)), and that the condition Sz(X) < ω1 yields the existence of an equivalent norm on X whose dual norm is locally uniformly convex. As an other application, we compute Sz… CONTINUE READING

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