Differences between the uniform diameter two properties
arXiv:2607.13788
summary
The paper defines uniform versions of the diameter‑two properties for Banach spaces via ultrapowers and proves that these uniform properties are all distinct from one another.
Abstract
We study uniform versions of the diameter two properties, that is, the uniform slice-D2P, the uniform D2P and the uniform SD2P, as the property that every ultrapower over any free ultrafilter over has the respective diameter two property. The aim of this note is to prove that all the uniform diameter two properties are different eachother.
21 pages
Topics & keywords
#diameter two property#uniform slice-d2p#ultrapower#banach space geometry#free ultrafilteruniform slice-D2Puniform D2Puniform SD2Pultrapowerfree ultrafilterdiameter two property