Abstract
Several Komlós like properties in Banach lattices are investigated. We prove that C(K) fails the \({oo}\)-pre-Komlós 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 dimension al Banach lattice E, there is an unbounded convex uo-pre-Komlós set C \({\subseteq E_{+}}\) which is not uo-Komlós.
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The authors are grateful to the anonymous referee for helpful comments.
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Emelyanov, E.Y., Erkurşun-Özcan, N. & Gorokhova, S.G. Komlós properties in Banach lattices. Acta Math. Hungar. 155, 324–331 (2018). https://doi.org/10.1007/s10474-018-0852-5
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DOI: https://doi.org/10.1007/s10474-018-0852-5
Key words and phrases
- Banach lattice
- o−convergence
- uo−convergence
- un-convergence
- Komlós property
- Komlós set
- space of continuous functions