Separable reduction of Frechet subdifferentiability in Asplund spaces

TL;DR

This paper introduces a new structural characterization of Asplund spaces to simplify and strengthen the analysis of Frechet subdifferentiability, employing rich families and logic models for separable reductions.

Contribution

It provides a novel structural characterization of Asplund spaces and applies it to simplify proofs and obtain isometrical results in the study of Frechet subdifferentiability.

Findings

Simplified proofs of Frechet subdifferentiability results

New structural characterization of Asplund spaces

Achieved isometrical results in the framework

Abstract

In the framework of Asplund spaces, we use two equivalent instruments - rich families and suitable models from logic - for performing separable reductions of various statements on Frechet subdifferentiability of functions. This way, isometrical results are actually obtained and several existed proofs are substantially simplified. Everything is based on a new structural characterization of Asplund spaces.