Unbounded Order Convergence and Universal Completions
We characterize vector lattices in which unbounded order convergence is eventually order bounded. Among other things, the characterization provides a solution to \cite[Probl.23]{Az}.
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arXiv subjects
S. G. Gorokhova
Publications and source records attributed to S. G. Gorokhova.
Komlos Properties in Banach Lattices
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 dimensional Banach lattice $E$ there is an unbounded convex $uo$-pre-Komlós set $C\subseteq E_+$ which is not $uo$-Komlós.
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Nonstandard Hulls of Lattice-Normed Ordered Vector Spaces
Nonstandard hulls of a vector lattice were introduced and studied in \cite{E10,E9,E7,E5,E3}. In recent paper \cite{EG}, these notions were extended to ordered vector spaces. In the present paper, following the construction of associated Banach-Kantorovich space \cite{E8}, we describe and investigate nonstandard hull of a lattice-normed space, which is a generalization of nonstandard hull of a normed space.
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