A non-type (D) operator in c0

TL;DR

This paper constructs a linear non-type (D) maximal monotone operator in the Banach space c0, challenging the previous belief that such operators are limited to certain classical spaces.

Contribution

The paper provides the first example of a linear non-type (D) maximal monotone operator in c0, expanding the understanding of the scope of these operators beyond classical spaces.

Findings

Constructed a linear non-type (D) operator in c0

Challenged the conjecture restricting non-type (D) operators to specific Banach spaces

Extended the class of spaces known to admit non-type (D) operators

Abstract

Previous examples of non-type (D) maximal monotone operators were restricted to $\ell^1$, $L^1$, and Banach spaces containing isometriccopies of these spaces. This fact led to the conjecture that non-type (D) operators were restricted to this class of Banach spaces. We present a linear non-type (D) operator in $c_0$.