Renormings of the dual of James tree spaces
Antonio Avil\'es
TL;DR
This paper investigates the renorming properties of the duals of James tree spaces, providing examples where certain renorming types are not possible despite the spaces being convexifiable.
Contribution
It presents new examples of James tree space duals with specific renorming properties, highlighting limitations in their geometric structure.
Findings
JT* admits no strictly convex renorming
JT* admits no Kadec renorming in certain cases
Some JT* are strictly convexifiable but lack Kadec renorming
Abstract
We discuss renorming properties of the dual of a James tree space JT. We present examples of weakly Lindelof determined JT such that JT* admits neither strictly convex nor Kadec renorming and of weakly compactly generated JT such that JT* does not admit Kadec renorming although it is strictly convexifiable.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Topology and Set Theory · Rings, Modules, and Algebras · Advanced Banach Space Theory