Some results on the convexity of the closure of the domain of a maximally monotone operator

TL;DR

This paper investigates the conditions under which the closure of the domain of a maximally monotone operator is convex, providing new insights and confirming a previously posed problem by Simons.

Contribution

It offers a concise analysis of convexity conditions for the domain closure of maximally monotone operators and resolves an open problem by Simons.

Findings

Confirmed convexity of the domain closure under certain conditions

Provided an affirmative answer to Simons' problem

Enhanced understanding of maximally monotone operator domains

Abstract

We provide a concise analysis about what is known regarding when the closure of the domain of a maximally monotone operator on an arbitrary real Banach space is convex. In doing so, we also provide an affirmative answer to a problem posed by Simons.