Abstract

We study the relations between some geometric properties of maximal monotone operators and generic geometric and analytical properties of the functions on the associate Fitzpatrick family of convex representations. We present some new technical properties of the Fitzpatrick families associated to bounded-range and bounded-domain maximal monotone operator which infer, among other properties, that the convex hull of the range of bounded domain maximal monotone operators are weak-* dense; we also present sufficient conditions for a convex function to represent a bounded-range maximal monotone operator; and finally give an example which makes clear that the result of Zagrodny that maximal monotone operators with a relatively compact range are of type (D) can not be extended to the weak* topology.

Author information

Contact details are reproduced from the original publication and may be historical.

Benar Fux Svaiter

Instituto de Matemática Pura e Aplicada, Estrada Dona Castorina 110, 22460-320 Rio de Janeiro, Brazil

benar@impa.br

Keywords

  • Fitzpatrick function
  • maximal monotone operator
  • bounded range
  • non-reflexive Banach spaces

Mathematics Subject Classification

47H05, 49J52, 47N10

References

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Suggested citation

B. F. Svaiter. “Geometric Properties of Maximal Monotone Operators and Convex Functions which May Represent Them.” Journal of Convex Analysis 21 (2014), No. 2, 553–569. https://doi.org/10.68381/jca21029

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Published by Heldermann Verlag, 2014. Rights now held by Banach Press.