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Operator minimax theorems in Banach lattices


Author: Carl G. Looney
Journal: Proc. Amer. Math. Soc. 65 (1977), 303-308
MSC: Primary 49B40; Secondary 47H99
MathSciNet review: 0451113
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Abstract: Let $ \psi :X \times Y \to (E, \leqslant ,\left\Vert \cdot \right\Vert)$, where X and Y are convex, X is compact, and E is a dedekind complete Banach lattice with unit e. If each $ \psi ( \cdot ,y)$ is continuous $ \leqslant $-concave on X, $ \{ \psi ( \cdot ,y):y \in Y\} $ is convex, and $ \psi (X \times Y)$ is minorized in E, then $ \sup \inf \psi (x,y) = \inf \sup \psi (x,y)$. Similar theorems are included.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1977-0451113-7
Keywords: Minimax theorem, Banach lattice, convex operator, convex sets, quasiconvex operators, Dinculeanu representation theorem
Article copyright: © Copyright 1977 American Mathematical Society