On Perturbed Substochastic Semigroups in Abstract State Spaces

  • Luisa Arlotti

    Università di Udine, Italy
  • B. Lods

    Università degli Studi di Torino, Italy
  • M. Mokhtar-Kharroubi

    Université de Franche-Comté, Besançon, France


The object of this paper is twofold: In the first part, we unify and extend the recent developments on honesty theory of perturbed substochastic semigroups (on L1(μ)L^{1}(\mu )-spaces or noncommutative L1L^{1} spaces) to general state spaces; this allows us to capture for instance a honesty theory in preduals of abstract von Neumann algebras or subspaces of duals of abstract CC^{\ast }-algebras. In the second part of the paper, we provide another honesty theory (a semigroup-perturbation approach) independent of the previous resolvent-perturbation approach and show the equivalence of the two approaches. This second viewpoint on honesty is new even in L1(μ)L^{1}(\mu ) spaces. Several fine properties of Dyson-Phillips expansions are given and a classical generation theorem by T. Kato is revisited.

Cite this article

Luisa Arlotti, B. Lods, M. Mokhtar-Kharroubi, On Perturbed Substochastic Semigroups in Abstract State Spaces. Z. Anal. Anwend. 30 (2011), no. 4, pp. 457–495

DOI 10.4171/ZAA/1444