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Proceedings of the American Mathematical Society

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

 

 

Continuity of nonlinear monotone operators


Author: S. P. Fitzpatrick
Journal: Proc. Amer. Math. Soc. 62 (1977), 111-116
MSC: Primary 47H05
DOI: https://doi.org/10.1090/S0002-9939-1977-0425687-6
MathSciNet review: 0425687
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Abstract: If a Banach space E has an equivalent norm such that 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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DOI: https://doi.org/10.1090/S0002-9939-1977-0425687-6
Article copyright: © Copyright 1977 American Mathematical Society