A maximal monotone operator of type (D) which maximal monotone extension to the bidual is not of type (D)

TL;DR

This paper introduces a family of linear type (D) operators with the property that their maximal monotone extensions to the bidual are not of type (D), challenging assumptions about their extension properties.

Contribution

It defines a new family of linear type (D) operators and provides a counterexample showing their extensions are not of type (D).

Findings

Inverse of maximal monotone extensions are not of type (D)

Provides explicit example within the defined family

Challenges previous assumptions about extension properties

Abstract

We define a family of linear type (D) operators for which the inverse of their maximal monotone extensions to the bidual are not of type (D) and provide an example of an operator in this family.