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Journal of Convex Analysis 12 (2005), No. 2, 417--429
Copyright Heldermann Verlag 2005

On Monotone Operators and Forms

Konrad Groh
Max-Planck-Institut f. Mathematik, Inselstr. 22, 04103 Leipzig, Germany

Consider a set-valued operator mapping points of a real Banach space into convex and weak* closed subsets of the dual space. It is shown that such operators can be investigated via the notion of a form. In particular, continuity, monotonicity, maximal monotonicity, and coerciveness are considered. Moreover, a calculus of forms is derived. Having established the above connections, a probably new sum theorem in nonreflexive Banach spaces is proved, and a Browder-type theorem for forms is given.

Keywords: Monotone operators, maximal monotone operators, representation, Browder theorem, nonreflexive sum theorem, bifunctions.

MSC: 47H05

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