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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Continuity properties of monotone nonlinear operators in locally convex spaces


Author: Dimitrios Kravvaritis
Journal: Proc. Amer. Math. Soc. 72 (1978), 46-48
MSC: Primary 47H05
MathSciNet review: 0487609
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Abstract: Let X be a real locally convex Hausdorff space, $ {X^\ast}$ its dual space, and T an operator from X into $ {2^{{X^\ast}}}$. The main results of this paper are: (i) if T is D-maximal monotone and locally bounded at each point of $ D(T)$, then T is upper demicontinuous; (ii) if X is a Fréchet space, T is monotone, and $ D(T)$ is open in X, then T is upper demicontinuous if and only if T is upper hemicontinuous, thus generalizing a result of [3].


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DOI: https://doi.org/10.1090/S0002-9939-1978-0487609-2
Keywords: Monotone and D-maximal monotone operators, local boundedness, quasi-denseness, upper demicontinuity, upper hemicontinuity
Article copyright: © Copyright 1978 American Mathematical Society