Two counterexamples to the spectral mapping theorem for semigroups of positive operators (Q1074092)

Let X be an \(L^ 1\)- or \(L^ 2\)-Banach lattice. Let \((W(t))_{t\geq 0}\) be a \(C_ 0\)-semigroup of positive operators on X with generator -T. Two examples of \(C_ 0\)-semigroups are presented for which the spectral identity \(e^{\sigma (-T)t}=\sigma (W(t))\setminus \{0\}\) fails for almost all \(t>0\). These examples were inspired by open problems from linear transport theory.