Extension operators on balls and on spaces of finite sets
Volume 227 / 2015
Studia Mathematica 227 (2015), 165-182
MSC: Primary 46B26, 46E15, 54C35, 54H05.
DOI: 10.4064/sm227-2-6
Abstract
We study extension operators between spaces of continuous functions on the spaces $\sigma _n(2^X)$ of subsets of $X$ of cardinality at most $n$. As an application, we show that if $B_H$ is the unit ball of a nonseparable Hilbert space $H$ equipped with the weak topology, then, for any $0<\lambda <\mu $, there is no extension operator $T: C(\lambda B_H)\to C(\mu B_H)$.
