2024/06/04 by Abraham Rueda Zoca, Zoca, Abraham Rueda · 1 citation
Engineering · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Mathematics #Functional Analysis (math.FA) #Heat Transfer and Optimization #Quantum Electrodynamics and Casimir Effect
paper · pdf · doi:10.48550/arxiv.2406.02129
openalex publication_date 2024/06/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this note we study the inheritance of the slice diameter two property by ultrapower spaces. Given a Banach space X, we give a characterisation of when (X)_\mathcal U, the ultrapower of X through a free ultrafilter \mathcal U, has the slice diameter two property obtaining that this is the case for many Banach spaces which are known to enjoy the slice diameter two property. We also provide, for every η>0, an example of a Banach space X with the Daugavet property such that the unit ball of (X)_\mathcal U contains a slice of diameter smaller than η for every free ultrafilter \mathcal U over \mathbb N. This proves, in particular, that the slice diameter two property is not in general inherited by taking ultrapower spaces.