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math.FA2025
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…
math.FA2025
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…
math.FA2025
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…