
Journal of Convex Analysis 12 (2005), No. 2, 417429 Copyright Heldermann Verlag 2005 On Monotone Operators and Forms Konrad Groh MaxPlanckInstitut f. Mathematik, Inselstr. 22, 04103 Leipzig, Germany konrad.groh@mis.mpg.de Consider a setvalued 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 Browdertype theorem for forms is given. Keywords: Monotone operators, maximal monotone operators, representation, Browder theorem, nonreflexive sum theorem, bifunctions. MSC: 47H05 [ Fulltextpdf (356 KB)] for subscribers only. 