2019/02/28 by Barroso, Cleon S., Gallagher, Torrey M.
#FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.1902.10852
We obtain a refinement of a selection principle for (K, λ)-wide-(s) sequences in Banach spaces due to Rosenthal. This result is then used to show that if C is a bounded, non-weakly compact, closed convex subset of a Banach space X, then there exists a Hausdorff vector topology τ on X which is weaker than the weak topology, a closed, convex τ-compact subset K of C and an affine bi-Lipschitz map T: K→ K without fixed points.