Separable determination of (generalized-)lushness

TL;DR

This paper proves that all Asplund lush spaces are also generalized-lush, using separable reduction techniques, addressing a question in the theory of Banach spaces.

Contribution

It establishes a link between lush and generalized-lush spaces in Asplund spaces through a novel separable reduction method.

Findings

All Asplund lush spaces are generalized-lush.

Provides a partial answer to Hardtke's question.

Introduces a separable reduction approach for this problem.

Abstract

We prove that every Asplund lush space is generalized-lush using the method of separable reduction. This gives a partial positive answer to a question by Jan-David Hardtke.