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On the range of a coercive maximal monotone operator in a nonreflexive Banach space


Author: Jean-Pierre Gossez
Journal: Proc. Amer. Math. Soc. 35 (1972), 88-92
MSC: Primary 47H05
DOI: https://doi.org/10.1090/S0002-9939-1972-0298492-7
MathSciNet review: 0298492
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Abstract: It is shown that the range of a coercive everywhere defined maximal monotone operator from a (nonreflexive) Banach space into its dual is dense for the $ \mathrm{weak}^*$ topology but not necessarily for the norm topology.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0298492-7
Keywords: Nonreflexive Banach space, maximal monotone operator, density of the range, bidual space, monotone extensions, Bishop-Phelps theorem, subdifferential
Article copyright: © Copyright 1972 American Mathematical Society

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