The modulus semigroup for linear delay equations II


The main purpose of this paper is describing the generator of the modulus semigroup of the C<sub>0</sub>-semigroup associated with the delay equation (Error rendering LaTeX formula) in the Banach lattice X L<sub>p</sub>(-h,0; X), where X is a Banach lattice with order continuous norm. As a preparation it is shown that W<sup>1</sup><sub>p</sub>(a,b; X) is a sublattice of L<sub>p</sub>(a,b; X), for 1 ≤ p < ∈fty. 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 C<sub>0</sub>-semigroups acting in KB-spaces.

DOI Code: 10.1285/i15900932v25n2p191

Keywords: Functional differential equation; Modulus semigroup; Perturbation theory

Classification: 47D06; 34k06; 47B60

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