This is an announcement for the paper "Extension operators on balls and on spaces of finite sets" by Antonio Aviles and Witold Marciszewski.

Abstract: We study extension operators between 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 $T: C(\lambda B_H)\to C(\mu B_H)$.

Archive classification: math.FA math.GN

Mathematics Subject Classification: 46B26, 46E15, 54C35, 54H05

Submitted from: avileslo@um.es

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1502.01875

or

http://arXiv.org/abs/1502.01875