\(C_0\)-semigroups norm continuous at infinity
The authors study a class of \(C_0\)-semigroups for which the spectral mapping theorem holds and the spectral bound and growth bound coincide. The crucial condition is norm continuity ``at infinity'' which means that \[ \lim_{t\to\infty} \limsup_{s\to 0}\| e^{-t\omega(A)} T(t)(I- e^{-s\omega(A)}T(s))\|= 0. \]
scientific article; zbMATH DE number 858475
scientific article