Remarks on $p$-monotone operators

TL;DR

This paper explores properties of $p$-monotone operators, including their extensions, linear cases, and the preservation of $p$-monotonicity under the Brezis-Browder theorem in reflexive Banach spaces.

Contribution

It provides new insights into $p$-monotone operators, characterizing their extensions, linear cases, and stability under key theorems.

Findings

Characterization of $p$-monotone operators with convex graphs

Conditions for linear $p$-monotone operators and their maximality

Proof that the Brezis-Browder theorem preserves $p$-monotonicity in reflexive spaces

Abstract

In this paper, we deal with three aspects of $p$-monotone operators. First we study $p$-monotone operators with a unique maximal extension (called pre-maximal), and with convex graph. We then deal with linear operators, and provide characterizations of $p$-monotonicity and maximal $p$-monotonicity. Finally we show that the Brezis-Browder theorem preserves $p$-monotonicity in reflexive Banach spaces.