2 citations · 9 across the 17 of their papers we have counts for
18 papers
Variants of order semicontinuity in Banach lattices
Eugene Bilokopytov
In this article we consider various properties of a normed lattice, which are similar to semicontinuity (also known as the Fatou property), establish relations between these proper…
A universal approximation theorem and its applications to vector lattice theory
Eugene Bilokopytov, Foivos Xanthos
A classical result in approximation theory states that for any continuous function \( φ: \mathbb{R} \to \mathbb{R} \), the set \( \operatorname{span}\{φ\circ g : g \in \operatornam…
Norm-attaining lattice homomorphisms and renormings of Banach lattices
Eugene Bilokopytov, Enrique García-Sánchez, David de Hevia +2
A well-known theorem due to R. C. James states that a Banach space is reflexive if and only if every bounded linear functional attains its norm. In this note we study Banach lattic…
Disjointly non-singular operators and various topologies on Banach lattices
Eugene Bilokopytov
We continue the study of dispersed subspaces and disjointly non-singular (DNS) operators on Banach lattices using topological methods. In particular, we provide a simple proof of t…
Locally hulled topologies
Eugene Bilokopytov
We present a general result about generating group topologies by pseudo-norms. Namely, we show that if a topology has a base of sets which are closed in a certain sense, then it ca…
Composition of locally solid convergences
Eugene Bilokopytov
We carry on a more detailed investigation of the composition of locally solid convergences as introduced in [BCTvdW24], as well as the corresponding notion of idempotency considere…