Linear Monotone Subspaces of Locally Convex Spaces

TL;DR

This paper investigates multi-valued linear monotone operators in locally convex spaces, analyzing their properties using Fitzpatrick and Penot functions, and establishing criteria for maximal monotonicity, uniqueness, and representability.

Contribution

It introduces new criteria for maximal monotonicity and representability of multi-valued linear monotone operators in locally convex spaces.

Findings

Criteria for maximal monotonicity established

Conditions for (dual-) representability derived

Analysis of uniqueness and negative-infimum properties

Abstract

The main focus of this paper is to study multi-valued linear monotone operators in the contexts of locally convex spaces via the use of their Fitzpatrick and Penot functions. Notions such as maximal monotonicity, uniqueness, negative-infimum, and (dual-) representability are studied and criteria are provided.