Linear $L$-positive sets and their polar subspaces

TL;DR

This paper introduces the concept of Banach SNL spaces and linear L-positive subsets, providing simplified proofs of existing theorems including the Brezis-Browder theorem, thereby advancing the theoretical understanding of these structures.

Contribution

It defines Banach SNL spaces and develops the theory of linear L-positive subsets, offering new simplified proofs of key results in the field.

Findings

Simplified proofs of recent results by Bauschke et al.

New theoretical framework for Banach SNL spaces.

Extension of classical theorems like Brezis-Browder.

Abstract

In this paper, we define a Banach SNL space to be a Banach space with a certain kind of linear map from it into its dual, and we develop the theory of linear $L$-positive subsets of Banach SNL spaces with Banach SNL dual spaces. We use this theory to give simplified proofs of some recent results of Bauschke, Borwein, Wang and Yao, and also of the classical Brezis-Browder theorem.