Characterisation of the weak-star symmetric strong diameter 2 property in Lipschitz spaces

TL;DR

This paper characterizes the weak* symmetric strong diameter 2 property in Lipschitz spaces, revealing differences from the weak* strong diameter 2 property and answering an open question in the field.

Contribution

It provides a new characterization of the weak* symmetric strong diameter 2 property in Lipschitz spaces based on metric space properties, distinguishing it from related properties.

Findings

The weak* symmetric strong diameter 2 property is characterized in terms of the underlying metric space.

It is shown that this property differs from the weak* strong diameter 2 property in Lipschitz spaces.

The paper answers a previously open question regarding the relationship between these properties.

Abstract

We give a characterisation of the weak* symmetric strong diameter 2 property for Lipschitz function spaces in terms of a property of the corresponding metric space. Using this characterisation we show that the weak* symmetric strong diameter 2 property is different from the weak* strong diameter 2 property in Lipschitz spaces, thereby answering a question posed in a recent paper by Haller, Langemets, Lima, and Nadel.