Vol. 33, No. 2, 1970

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On dispersive operators in Banach lattices

Ken iti Sato

Vol. 33 (1970), No. 2, 429–443

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.

Mathematical Subject Classification
Primary: 47.50
Secondary: 46.00
Received: 19 May 1969
Published: 1 May 1970
Ken iti Sato