Banach SSD spaces and classes of monotone sets

TL;DR

This paper unifies various classes of maximally monotone sets through the theory of SSD spaces and strongly representable sets, showing their equivalence and deriving properties from known concepts.

Contribution

It establishes the equivalence of multiple classes of maximally monotone sets and connects their properties via the unified framework of SSD and strongly representable sets.

Findings

Type (ED), dense type, type (D), type (NI), and strongly representable are equivalent concepts.

Properties of strongly representable sets follow from properties of sets of type (ED).

Unified framework simplifies understanding of maximally monotone sets.

Abstract

In this paper, we unify the theory of SSD spaces and the theory of strongly representable sets, and we apply our results to the theory of the various classes of maximally monotone sets. In particular, we prove that type (ED), dense type, type (D), type (NI) and strongly representable are equivalent concepts and, consequently, that the known properties of strongly representable sets follow from known properties of sets of type (ED).