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arXiv · 1902.10852

Selection type results and fixed point property for affine bi-Lipschitz maps

Cleon S. Barroso·Torrey M. Gallagher
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Abstract

We obtain a refinement of a selection principle for $(\mathcal{K}, \lambda)$-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 $\tau$ on $X$ which is weaker than the weak topology, a closed, convex $\tau$-compact subset $K$ of $C$ and an affine bi-Lipschitz map $T: K\to K$ without fixed points.

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Cleon S. Barroso, Torrey M. Gallagher. 2019-02-28. Selection type results and fixed point property for affine bi-Lipschitz maps. https://arxiv.org/abs/1902.10852

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