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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
DOI: https://doi.org/10.1090/S0002-9939-1985-0781064-4
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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Article copyright: © Copyright 1985 American Mathematical Society