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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Continuity of maximal monotone sets in Banach space


Author: R. E. Showalter
Journal: Proc. Amer. Math. Soc. 42 (1974), 543-546
MSC: Primary 47H05
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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1974-0333850-5
PII: S 0002-9939(1974)0333850-5
Article copyright: © Copyright 1974 American Mathematical Society