On Schrödinger semigroups and related topics

Abstract

This paper deals with two related subjects. In the first part, we give generation theorems, relying on (weak) compactness arguments, for perturbed positive semigroups in general ordered Banach spaces with additive norm on the positive cone. The second part provides new functional analytic developments on semigroup theory for Schrödinger operators in L p spaces with ( L 1 ) Δ-bounded potentials without restriction on the ( L 1 ) Δ-bound. In particular, our formalism enlarges a priori the classical Kato class and its subsequent refinements. The connection with form-perturbation theory is also dealt with.