Abstract

Gossez type (D) operators are defined in non-reflexive Banach spaces and share with the subdifferential operator a topological related property, characterized by bounded nets. In this work we present new properties and characterizations of these operators. The class (NI) was defined after Gossez defined the class (D) and seemed to generalize the class (D). One of our main results is the proof that these classes, type (D) and (NI), are identical.

Author information

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Maicon Marques Alves

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

maicon@impa.br

Benar Fux Svaiter

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

benar@impa.br

Keywords

  • Maximal monotone operators
  • Gossez type (D) operators
  • non-reflexive Banach spaces
  • nets
  • Fitzpatrick functions

Mathematics Subject Classification

47H05, 46T99, 47N10

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Suggested citation

M. Marques Alves, B. F. Svaiter. “On Gossez Type (D) Maximal Monotone Operators.” Journal of Convex Analysis 17 (2010), No. 3&4, 1077–1088. https://doi.org/10.68381/jca17066

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Published by Heldermann Verlag, 2010. Rights now held by Banach Press.