Dispersive operators were
introduced by R. S. Phillips for characterization of infinitesimal generators of
nonnegative contraction semigroups in Banach lattices. Later other definitions of
dispersiveness were given by M. Hasegawa and K. Sato. H. Kunita, for the
purpose of application to Markov processes, introduced the notion of complete
γ-dispersiveness which characterizes the infinitesimal generators of e-majoration
preserving nonnegative semigroups Tt with norm ≦ eγt. In this paper we will give
a unified treatment of these results. Further, we will clarify the relation
between dispersiveness and dissipativeness in some cases. We consider also
characterization of infinitesimal generators of nonnegative semigroups without norm
conditions.
