A minimax theorem for functions taking values in a Riesz space
type: Item
instance of: scholarly article
title: A minimax theorem for functions taking values in a Riesz space
zbMATH Open document ID: 0651.49005
DOI: 10.1016/0022-247X(88)90360-5
author: Anna Martellotti
author: Anna Salvadori
published in: Journal of Mathematical Analysis and Applications
publication date: 1988-01-01T00:00:00Z
review text: Let \((E,C)\) be an order-complete topological Riesz space, where \(C\) is the positive cone. The objective of the paper is to formulate the following Riesz space version of a Hahn-Banach type theorem proved by \textit{B. Fuchssteiner} and \textit{H. König} for real functions [General inequalities 2, Proc. 2nd int. Conf., Oberwolfach 1978, ISNM Vol. 47, 255--266 (1980; Zbl 0452.46002)]: Let \(F\) be a real vector space, \(\vartheta\colon F\to (E,C)\) be a sublinear operator and let \(G\) be a nonempty subset of \(F\) verifying some suitable assumptions of `convexity' type. If \(\vartheta|_G\geq 0\), then there is a linear operators \(\phi\colon F\to E\) such that \(\phi\leq \vartheta\) and \(\vartheta|_G\geq 0\). Then as a consequence of this theorem, some minimax theorems in Riesz space are given, under very general convexity assumptions.
Mathematics Subject Classification ID: 49J35
Mathematics Subject Classification ID: 46A40
Mathematics Subject Classification ID: 49J27
Mathematics Subject Classification ID: 46A22
zbMATH DE Number: 4062006
zbMATH Keywords: order-complete topological Riesz space
zbMATH Keywords: minimax theorems
reviewed by: Calogero Vinti
MaRDI profile type: Publication
cites work: Q3899001
cites work: Über das von-Neumannsche Minimax-Theorem
cites work: Q5555984
cites work: Q5613420
description: scientific article; zbMATH DE number 4062006