On Gossez type (D) maximal monotone operators

TL;DR

This paper investigates Gossez type (D) maximal monotone operators in non-reflexive Banach spaces, providing new properties and showing that classes (D) and (NI) are actually the same, thus clarifying their relationship.

Contribution

It introduces new properties and characterizations of Gossez type (D) operators and proves the equivalence of classes (D) and (NI).

Findings

Classes (D) and (NI) are identical.

New properties of Gossez type (D) operators are established.

Enhanced understanding of maximal monotone operators in non-reflexive spaces.

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.