On duality and spectral properties of (a, k)-regularized resolvents

Abstract

We construct a duality theory for (a, k)-regularized resolvents, extending some of the known theorems for dual semigroups. We present several classes of spaces, which in the semigroup case correspond to the Favard class and the sun-dual space. By duality arguments spectral inclusion theorems for regularized resolvents are also obtained.