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27 April 2024
 
  » arxiv » 1710.2580

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Komlos Properties in Banach Lattices
E. Y. Emelyanov ; N. Erkursun Ozcan ; S. G. Gorokhova ;
Date 6 Oct 2017
AbstractSeveral 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 $uin U$ 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 $Csubseteq E_+$ which is not $uo$-Koml’os.
Source arXiv, 1710.2580
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