Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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?)

  • [1] F. E. Browder, Multivalued monotone nonlinear mappings and duality mappings in Banach spaces, Trans. Amer. Math. Soc. 118 (1965), 338-351. MR 31 #5114. MR 0180884 (31:5114)
  • [2] -, Nonlinear variational inequalities and maximal monotone mappings in Banach spaces, Math. Ann. 183 (1969), 213-231. MR 42 #6661. MR 0271780 (42:6661)
  • [3] T. Kato, Demicontinuity, hemicontinuity and monotonicity. II, Bull. Amer. Math. Soc. 73 (1967), 886-889. MR 38 #6411. MR 0238135 (38:6411)
  • [4] P. M. Fitzpatrick, P. Hess and T. Kato, Local boundedness of monotone-type operators, Proc. Japan Acad. 48 (1972), 275-277. MR 0312336 (47:898)
  • [5] R. T. Rockafellar, Local boundedness of nonlinear, monotone operators, Michigan Math. J. 16 (1969), 397-407. MR 40 #6229. MR 0253014 (40:6229)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 47H05

Retrieve articles in all journals with MSC: 47H05

Additional Information

Article copyright: © Copyright 1974 American Mathematical Society

American Mathematical Society