Estimation of the Szlenk index of reflexive Banach spaces using generalized Baernstein spaces

Ryan Causey

Estimation of the Szlenk index of reflexive Banach spaces using generalized Baernstein spaces

Functional Analysis 2013-08-27 v1

Authors: Ryan Causey

Abstract

For each ordinal $\alpha< \omega_1$ , we prove the existence of a separable, reflexive Banach space with a basis and Szlenk index $\omega^{\alpha+1}$ which is universal for the class of separable, reflexive Banach spaces $X$ such that the Szlenk indices $Sz(X), Sz(X^*)$ do not exceed $\omega^\alpha$ .

Keywords

Szlenk index reflexive Banach spaces generalized Baernstein spaces separable Banach spaces ordinal numbers universal space basis

Cite

@article{arxiv.1308.5416,
  title  = {Estimation of the Szlenk index of reflexive Banach spaces using generalized Baernstein spaces},
  author = {Ryan Causey},
  journal= {arXiv preprint arXiv:1308.5416},
  year   = {2013}
}

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arXiv admin note: text overlap with arXiv:1212.5576

Estimation of the Szlenk index of reflexive Banach spaces using generalized Baernstein spaces

Abstract

Keywords

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