Structure theory for maximally monotone operators with points of continuity

TL;DR

This paper develops explicit structure formulas for maximally monotone operators with nonempty interior domains in Banach spaces, providing new proofs of key properties and exploring applications and examples.

Contribution

It introduces new explicit structure formulas for such operators and offers alternative proofs for their closedness and property (Q).

Findings

New structure formulas for maximally monotone operators.

Alternative proofs of norm-to-weak* closedness and property (Q).

Applications and examples illustrating the theory.

Abstract

In this paper, we consider the structure of maximally monotone operators in Banach space whose domains have nonempty interior and we present new and explicit structure formulas for such operators. Along the way, we provide new proofs of the norm-to-weak$^{*}$ closedness and of property (Q) for these operators (as recently proven by Voisei). Various applications and limiting examples are given.