The Riesz-Kantorovich formula and general equilibrium theory
type: Item
instance of: scholarly article
title: The Riesz-Kantorovich formula and general equilibrium theory
zbMATH Open document ID: 0977.91012
DOI: 10.1016/S0304-4068(99)00041-5
published in: Journal of Mathematical Economics
publication date: 2000-08-14T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 91B02
Mathematics Subject Classification ID: 91B50
zbMATH DE Number: 1491284
zbMATH Keywords: supremum
zbMATH Keywords: Riesz-Kantorovich formula
author: Charalambos D. Aliprantis
author: R. Tourky
author: Nicholas C. Yannelis
MaRDI profile type: Publication
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full work available at URL: s0304-4068(99)00041-5
OpenAlex ID: W2086816484
description: scientific article; zbMATH DE number 1491284