Operator minimax theorems in Banach lattices
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- by Carl G. Looney PDF
- Proc. Amer. Math. Soc. 65 (1977), 303-308 Request permission
Abstract:
Let $\psi :X \times Y \to (E, \leqslant ,\left \| \cdot \right \|)$, 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
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Additional Information
- © Copyright 1977 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 65 (1977), 303-308
- MSC: Primary 49B40; Secondary 47H99
- DOI: https://doi.org/10.1090/S0002-9939-1977-0451113-7
- MathSciNet review: 0451113