Continuity properties of monotone nonlinear operators in locally convex spaces

Kravvaritis, Dimitrios

doi:10.1090/S0002-9939-1978-0487609-2

Continuity properties of monotone nonlinear operators in locally convex spaces
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by Dimitrios Kravvaritis

Proc. Amer. Math. Soc. 72 (1978), 46-48

DOI: https://doi.org/10.1090/S0002-9939-1978-0487609-2

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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].

References

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