Proceedings of the Royal Society of Edinburgh: Section A Mathematics

Research Article

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

Carlos Lizamaa1 and Humberto Pradoa1

a1 Departamento de Matemática, Universidad de Santiago de Chile, Casilla 307, Correo-2, Santiago, Chile (clizama@usach.cl; hprado@usach.cl)

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.

(Received March 19 2007)

(Accepted June 17 2008)