Symmetric strong diameter two property
Journal article, Peer reviewed
Accepted version
View/ Open
Date
2019Metadata
Show full item recordCollections
- Institutt for IKT og realfag [601]
- Publikasjoner fra CRIStin - NTNU [38688]
Original version
Mediterranean Journal of Mathematics. 2019, 16:35 (2), 1-17. 10.1007/s00009-019-1306-1Abstract
We study Banach spaces with the property that, given a finite number of slices of the unit ball, there exists a direction such that all these slices contain a line segment of length almost 2 in this direction. This property was recently named the symmetric strong diameter two property by Abrahamsen, Nygaard, and P˜oldvere. The symmetric strong diameter two property is not just formally stronger than the strong diameter two property (finite convex combinations of slices have diameter 2). We show that the symmetric strong diameter two property is only preserved by `∞-sums, and working with weak star slices we show that Lip0 (M) have the weak star version of the property for several classes of metric spaces M.