On perturbed substochastic semigroups in abstract state spaces
Luisa Arlotti, Bertrand Lods, Mustapha Mokhtar-Kharroubi, (LM-Besan\c{c}on)

TL;DR
This paper develops a generalized honesty theory for perturbed substochastic semigroups across various abstract state spaces, unifying existing approaches and introducing a novel semigroup-perturbation perspective.
Contribution
It extends honesty theory to general state spaces, including noncommutative spaces, and introduces a new perturbation approach that is shown to be equivalent to existing methods.
Findings
Unified honesty theory for various state spaces
Introduction of a new semigroup-perturbation honesty approach
Revisiting classical generation theorems with new insights
Abstract
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.
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Taxonomy
TopicsAdvanced Banach Space Theory · Stochastic processes and financial applications · Approximation Theory and Sequence Spaces
