Continuity of nonlinear monotone operators

Fitzpatrick, S. P.

doi:10.1090/S0002-9939-1977-0425687-6

Continuity of nonlinear monotone operators
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by S. P. Fitzpatrick

Proc. Amer. Math. Soc. 62 (1977), 111-116

DOI: https://doi.org/10.1090/S0002-9939-1977-0425687-6

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Abstract:

If a Banach space E has an equivalent norm such that $\text {weak}^\ast$ sequential convergence and norm convergence coincide on the dual unit sphere, then every monotone operator on E is single-valued and norm-norm continuous on a dense ${G_\delta }$ subset of E. In particular, this holds for reflexive spaces.

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Lectures on analysis

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