On Gossez type (D) maximal monotone operators

Abstract

Gossez type (D) operators are defined in non-reflexive Banach spaces and share with the subdifferential 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.

Added one reference. Added Corollary 4.3, which is a trivial, but interesting, consequence of Lemma 4.1 and Theorem 4.2

References in corpus (3)

• A new old class of maximal monotone operators
• Maximal monotone operators with a unique extension to the bidual
• On the surjectivity properties of perturbations of maximal monotone operators in non-reflexive Banach spaces

Cited by in corpus (12)

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• Polar subspaces and automatic maximality
• The Brézis-Browder Theorem in a general Banach space
• Location, identification, and representability of monotone operators in locally convex spaces
• Characterizations of ultramaximally monotone operators
• Lower Limits of Type (D) Monotone Operators in general Banach Spaces
• On the generalized parallel sum of two maximal monotone operators of Gossez type (D)
• Every maximally monotone operator of Fitzpatrick-Phelps type is actually of dense type
• Geometric properties of maximal monotone operators and convex functions which may represent them
• Construction of pathological maximally monotone operators on non-reflexive Banach spaces