The Br\'ezis-Browder Theorem in a general Banach space

TL;DR

This paper extends the classical Brézis-Browder theorem, which characterizes maximal monotonicity in reflexive spaces, to the broader setting of general Banach spaces, providing a more comprehensive understanding of monotone linear relations.

Contribution

The paper generalizes the Brézis-Browder theorem from reflexive spaces to all Banach spaces, refining the characterization of maximal monotonicity for linear relations.

Findings

Extended the theorem to non-reflexive Banach spaces

Provided new criteria for maximal monotonicity in general Banach spaces

Enhanced understanding of linear relations in functional analysis

Abstract

During the 1970s Br\'ezis and Browder presented a now classical characterization of maximal monotonicity of monotone linear relations in reflexive spaces. In this paper, we extend and refine their result to a general Banach space.