Lectures on maximal monotone operators

TL;DR

This paper provides a comprehensive, self-contained exposition of classical and recent results on maximal monotone operators in Banach spaces, emphasizing open problems especially in nonreflexive spaces.

Contribution

It offers an accessible lecture-based overview of maximal monotone operators, highlighting fundamental properties and open questions in nonreflexive Banach spaces.

Findings

Summarizes classical and recent facts about maximal monotone operators.

Highlights open problems in nonreflexive Banach spaces.

Provides educational material for advanced mathematical study.

Abstract

This is a 30 page set of lecture notes, in Plain TeX, which were prepared for and presented as a series of lectures (10 1/2 hours over two weeks) at the 2nd Summer School on Banach Spaces, Related Areas and Applications in Prague and Paseky, Czech Republic, during August, 1993. They consist of a largely self-contained exposition of both classical and recent basic facts about maximal monotone operators on Banach spaces, motivated in part by the goal of highlighting several fundamental properties of such operators which remain open questions in nonreflexive Banach spaces.