  Consider probabilistic distributions on the space of infinite Hermitian
matrices $Herm(\infty)$ invariant with respect to the unitary group
$U(\infty)$. We describe the closure of $U(\infty)$ in the space of spreading
maps (polymorphisms) of $Herm(\infty)$, this closure is a semigroup isomorphic
to the semigroup of all contractive operators.
