Komlos Properties in Banach Lattices

E. Y. Emelyanov; N. Erkursun Ozcan; S. G. Gorokhova

Komlos Properties in Banach Lattices

Functional Analysis 2017-10-10 v1

Authors: E. Y. Emelyanov , N. Erkursun Ozcan , S. G. Gorokhova

Abstract

Several Koml\'os like properties in Banach lattices are investigated. We prove that $C(K)$ fails the $oo$ -pre-Koml\'os property, assuming that the compact Hausdorff space $K$ has a nonempty separable open subset $U$ without isolated points such that every $u\in U$ has countable neighborhood base. We prove also that for any infinite dimensional Banach lattice $E$ there is an unbounded convex $uo$ -pre-Koml\'os set $C\subseteq E_+$ which is not $uo$ -Koml\'os.

Keywords

banach space properties banach spaces

Cite

@article{arxiv.1710.02580,
  title  = {Komlos Properties in Banach Lattices},
  author = {E. Y. Emelyanov and N. Erkursun Ozcan and S. G. Gorokhova},
  journal= {arXiv preprint arXiv:1710.02580},
  year   = {2017}
}

Comments

8 pages

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