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

 

On the range of the sum of monotone operators
in general Banach spaces


Author: Hassan Riahi
Journal: Proc. Amer. Math. Soc. 124 (1996), 3333-3338
MSC (1991): Primary 47H05; Secondary 46B10, 35J60
MathSciNet review: 1322938
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Abstract: The purpose of this paper is to generalize the Brézis-Haraux theorem on the range of the sum of monotone operators from a Hilbert space to general Banach spaces. The result obtained provides that the range $\mathcal R(\overline {A+B}{}^\tau )$ is topologically almost equal to the sum $\mathcal R(A)+\mathcal R(B)$ where $\tau $ is a compatible topology in $X^{**}\times X^*$ as proposed by Gossez. To illustrate the main result we consider some basic properties of densely maximal monotone operators.


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Additional Information

Hassan Riahi
Affiliation: Semlalia Faculty of Sciences, Mathematics, University Cadi Ayyad, Boulevard My Abdellah, B.P.S. 15, 40 000 Marrakesh, Morocco

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03314-X
PII: S 0002-9939(96)03314-X
Keywords: Banach space, densely maximal monotone operator, $3^*$-monotone operator, range, subdifferential
Received by editor(s): April 18, 1994
Received by editor(s) in revised form: January 31, 1995
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1996 American Mathematical Society