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math.FA2021
Vector lattice approach to the Riesz and Stone Representation theorems
Eugene Bilokopytov
We present vector-lattice-theoretic proofs of Riesz Representation Theorem and Stone Representation Theorem.
math.FA2021
Order continuity and regularity on vector lattices and on lattices of continuous functions
Eugene Bilokopytov
We give several characterizations of order continuous vector lattice homomorphisms between Archimedean vector lattices. We reduce the proofs of some of the equivalences to the case…
math.FA2021
Disjointly non-singular operators on order continuous Banach lattices complement the unbounded norm topology
Eugene Bilokopytov
In this article we investigate the disjointly non-singular (DNS) operators. Following [8] we say that an operator from a Banach lattice into a Banach space is DNS, if n…