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Continuity of maximal monotone sets in Banach space


Author: R. E. Showalter
Journal: Proc. Amer. Math. Soc. 42 (1974), 543-546
MSC: Primary 47H05
DOI: https://doi.org/10.1090/S0002-9939-1974-0333850-5
MathSciNet review: 0333850
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Abstract: A monotone set-valued map of a Banach space to its dual is shown to map line segments into bounded sets. It follows that convergent sequences are mapped into bounded sets and, when the space is separable or reflexive, this imposes continuity requirements on maximal monotone maps.


References [Enhancements On Off] (What's this?)

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DOI: https://doi.org/10.1090/S0002-9939-1974-0333850-5
Article copyright: © Copyright 1974 American Mathematical Society

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