Relation between the boundary point spectrum of a generator and of its adjoint (Q1174350)

The authors investigate relations between the boundary point spectrum of the generator \(A\) of a \(C_ 0\)-semigroup \((T(t))_{t\geq 0}\) and its adjoint \(A^*\). These relations are of interest in the context of the stability results on \(C_ 0\)-semigroups of Lyubich-Phóng and Arendt- Batty. The results are obtained for the cases that \((T(t))\) is weakly almost periodic and, if \((T(t))\) is positive on a Banach lattice, that \((T(t))\) is submarkovian.