The modulus semigroup for linear delay equations II

Abstract

The main purpose of this paper is describing the generator of the modulus semigroup of the -semigroup associated with the delay equation (Error rendering LaTeX formula) in the Banach lattice , where X is a Banach lattice with order continuous norm. As a preparation it is shown that is a sublattice of , for . A further preparation is the computation of the modulus of the operator L appearing above. Also, we establish a result concerning the existence of the modulus semigroup for -semigroups acting in -spaces.