Location, identification, and representability of monotone operators in locally convex spaces

TL;DR

This paper investigates the intrinsic properties of monotone operators in locally convex spaces to understand conditions under which the sum of maximal monotone operators maintains maximality, focusing on domain interiority constraints.

Contribution

It extends the analysis of monotone operators to locally convex spaces, providing new insights into the sum conjecture under domain interiority conditions.

Findings

Characterization of monotone operators in locally convex spaces

Conditions ensuring the sum of maximal monotone operators remains maximal

Insights into the domain properties affecting operator sum maximality

Abstract

In this paper we study, in the relaxed context of locally convex spaces, intrinsic properties of monotone operators needed for the sum conjecture for maximal monotone operators to hold under classical interiority-type domain constraints.