Polar subspaces and automatic maximality

TL;DR

This paper investigates the structure of polar subspaces within Banach SN spaces, providing new theoretical results and improved proofs, with applications to monotone linear subspaces of Banach spaces and their duals.

Contribution

It introduces novel results on polar subspaces in Banach SN spaces and offers enhanced proofs for existing theorems, advancing the understanding of monotone subspaces.

Findings

New characterizations of polar subspaces

Improved proofs of known theorems

Applications to monotone linear subspaces

Abstract

This paper is about certain linear subspaces of Banach SN spaces (that is to say Banach spaces which have a symmetric nonexpansive linear map into their dual spaces). We apply our results to monotone linear subspaces of the product of a Banach space and its dual. In this paper, we establish several new results and also give improved proofs of some known ones in both the general and the special contexts.