Transactions of the American Mathematical Society

Author(s): S. Simons
Journal: Trans. Amer. Math. Soc. 350 (1998), 2953-2972.
MSC (1991): Primary 47H05, 46B10; Secondary 49J35, 46A30
Original article: Tran. Amer. Math. Soc. 350 (1998), no. 7, 2953-2972.
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Abstract: In this paper, we derive sufficient conditions for the sum of two or more maximal monotone operators on a reflexive Banach space to be maximal monotone, and we achieve this without any renorming theorems or fixed-point-related concepts. In the course of this, we will develop a generalization of the uniform boundedness theorem for (possibly nonreflexive) Banach spaces. We will apply this to obtain the Fenchel Duality Theorem for the sum of two or more proper, convex lower semicontinuous functions under the appropriate constraint qualifications, and also to obtain additional results on the relation between the effective domains of such functions and the domains of their subdifferentials. The other main tool that we use is a standard minimax theorem.

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Retrieve articles in Transactions of the American Mathematical Society with MSC (1991): 47H05, 46B10, 49J35, 46A30

S. Simons
Affiliation: Department of Mathematics, University of California, Santa Barbara, California 93106-3080
Email: simons@math.ucsb.edu

DOI: 10.1090/S0002-9947-98-02045-5
PII: S 0002-9947(98)02045-5
Keywords: Banach space, reflexivity, maximal monotone operator, sum theorem, constraint qualification, proper convex lower semicontinuous function, uniform boundedness theorem, Fenchel Duality Theorem, minimax theorem
Received by editor(s): July 16, 1996
Copyright of article: Copyright 1998, American Mathematical Society

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