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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Generic Fréchet differentiability of convex operators


Author: Nikolai K. Kirov
Journal: Proc. Amer. Math. Soc. 94 (1985), 97-102
MSC: Primary 46G05; Secondary 47H99, 90C25
MathSciNet review: 781064
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Abstract: We consider order-bounded convex operators $ F:E \to X$ from a reflexive Banach space $ E$ into a Banach lattice $ X$. In both cases (i) $ X$ and $ {X^*}$ have weak compact intervals, and (ii) $ X$ has norm compact intervals, we obtain that $ F$ is Fréchet differentiable at the points of some dense $ {G_\delta }$ subset of $ E$.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1985-0781064-4
PII: S 0002-9939(1985)0781064-4
Article copyright: © Copyright 1985 American Mathematical Society