Quasidensity: a survey and some examples

TL;DR

This paper surveys key results on quasidense multifunctions and subsets in Banach spaces, providing simple examples across various space types without detailed proofs.

Contribution

It offers a comprehensive overview of quasidensity concepts and illustrates them with basic examples in different Banach space settings.

Findings

Quasidense multifunctions relate to dual space properties.

Examples demonstrate quasidensity in Hilbert and Banach spaces.

Survey summarizes main results without proofs.

Abstract

In three previous papers, we discussed quasidense multifunctions from a Banach space into its dual, or, equivalently, quasidense subsets of the product of a Banach space and its dual. In this paper, we survey (without proofs) some of the main results about quasidensity, and give some simple limiting examples in Hilbert spaces, reflexive Banach spaces, and nonreflexive Banach spaces.