Journal of Convex Analysis 17 (2010), No. 3&4, 1077--1088
Copyright Heldermann Verlag 2010
On Gossez Type (D) Maximal Monotone Operators
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
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.
Keywords: Maximal monotone operators, Gossez type (D) operators, non-reflexive Banach spaces, nets, Fitzpatrick functions.
MSC: 47H05, 46T99, 47N10
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