Komlos Properties in Banach Lattices

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

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arXiv · 1710.02580

Komlos Properties in Banach Lattices

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

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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.

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BibTeX RIS

E. Y. Emelyanov, N. Erkursun Ozcan, S. G. Gorokhova. 2017-10-06. Komlos Properties in Banach Lattices. https://arxiv.org/abs/1710.02580

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