Motivated by the operad built from moduli spaces of Riemann surfaces, we
consider a general class of operads in the category of spaces that satisfy
certain homological stability conditions. We prove that such operads are
infinite loop space operads in the sense that the group completions of their
algebras are infinite loop spaces.
The recent, strong homological stability results of Galatius and
Randal-Williams for moduli spaces of even dimensional manifolds can be used to
construct examples of operads with homological stability. As a consequence the
map to $K$-theory defined by the action of the diffeomorphisms on the middle
dimensional homology can be shown to be a map of infinite loop spaces.