  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 $T: C(\lambda
B_H)\to C(\mu B_H)$.
