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 -spaces or noncommutative 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 -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 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. 457–495DOI 10.4171/ZAA/1444