The Riesz-Kantorovich formula and general equilibrium theory
This paper adresses the question: Is there an example of a pair of order-bounded linear functionals \(f\) and \(g\) for which the supremum \(f\vee g\) exists but does not satisfy the Riesz-Kantorovich formula? The authors consider an arbitrary ordered vector space \(L\) with order unit and weakly compact order intervals. If \(f\) and \(g\) are continuous linear functionals on \(L\) and \(f\vee g\) exists in the order dual \(L^\sim\), then \(f\vee g\) must satisfy the Riesz-Kantorovich formula. In addition, the authors demonstrate that if \(L\) is locally convex with weakly compact intervals, then \(f\vee g\) exists in \(L^\sim\) for any pair of continuous linear functionals \(f\) and \(g\) if and only if \(L\) has the Riesz decomposition property.
scientific article; zbMATH DE number 1491284
scientific article