A generalization of Riesz homomorphisms on order unit spaces

Riesz homomorphisms on vector lattices have been generalized to Riesz* homomorphisms on ordered vector spaces by van Haandel using a condition on sets of finitely many elements. Van Haandel attempted to prove that it suffices to take sets of two elements. We show that this is not true, in general. T...

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Bibliographic Details
Published in:Quaestiones mathematicae 2024-09, Vol.47 (9), p.1887-1911
Main Authors: Boisen, Florian, Hölker, Valentin G., Kalauch, Anke, Stennder, Janko, van Gaans, Onno
Format: Article
Language:English
Subjects:
functional representation
Homomorphisms
order unit space
ordered vector space
Riesz homomorphism
Vector spaces
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Summary:Riesz homomorphisms on vector lattices have been generalized to Riesz* homomorphisms on ordered vector spaces by van Haandel using a condition on sets of finitely many elements. Van Haandel attempted to prove that it suffices to take sets of two elements. We show that this is not true, in general. The description by two elements motivates to introduce mild Riesz* homomorphisms. We investigate their properties on order unit spaces, where the geometry of the dual cone plays a crucial role. Hereby, we mostly focus on the finite-dimensional case.
ISSN:1607-3606
1727-933X
DOI:10.2989/16073606.2024.2346245