Abstract
The main purpose of this paper is describing the generator of the modulus semigroup of the C0-semigroup associated with the delay equation ( 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. As a preparation it is shown that W 1 p(a, b; X) is a sublattice of Lp(a, b; X), for 1 ≤ p < ∞. 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 C0- semigroups acting in KB-spaces.
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