The modulus semigroup for linear delay equations III

In this paper, we describe the modulus semigroup of the C0-semigroup associated with the linear differential equation with delay u′(t)=Au(t)+Lut(t⩾0),u(0)=x∈X,u0=f∈Lp(-h,0;X),in the Banach lattice X×Lp(-h,0;X), where X is a Banach lattice with order continuous norm. The progress with respect to previous papers is that A may be an unbounded generator of a C0-semigroup possessing a modulus semigroup.