Admissible subspaces and the denseness of the intersection of the domains of semigroup generators


Let Ti = {Ti(t): t ≥ 0} be a (C0) semigroup of linear operators on a Banach space X, with infinitesimal generator Ai, i = 1, 2. If Y is a dense Banachable subspace of X left invariant by T1 then it is shown that in many cases D(A1) ∩ Y is dense in X, where D(A1) is the domain of A1. In particular, if X is either separable or reflexive and if T1 leaves D(A2) invariant, then D(A1 ∩ D(A2) is dense in X. © 1972.

Publication Title

Journal of Functional Analysis