Evaluating characterizations of homomorphisms on truncated vector lattices of functions

2020/04/04 by Karim Boulabiar, Boulabiar, Karim, Sameh Bououn +1
Mathematics · #Advanced Banach Space Theory #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2004.01835

openalex publication_date 2020/04/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let L be a (non necessarily unital) truncated vector lattice of real-valued functions on a nonempty set X. A nonzero linear functional ψ on L is called a truncation homomorphism if it preserves truncation, i.e.,% ψ( f\wedge1_X) =min\ ψ( f) ,1\ for all f∈ L. We prove that a linear functional ψ on L is a truncation homomorphism if and only if ψ is a lattice homomorphism and% sup\ ψ( f) :f≤1_X\ =1. This allows us to prove different evaluating characterizations of truncation homomorphisms. In this regard, a special attention is paid to the continuous case and various results from the existing literature are generalized.

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