Abstract

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.

Author information

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Keywords

  • Monotone operators
  • maximal monotone operators
  • representation
  • Browder theorem
  • nonreflexive sum theorem
  • bifunctions

Mathematics Subject Classification

47H05

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Suggested citation

K. Groh. “On Monotone Operators and Forms.” Journal of Convex Analysis 12 (2005), No. 2, 417–429. https://doi.org/10.68381/jca12029

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Published by Heldermann Verlag, 2005. Rights now held by Banach Press LLC.