Spectral mapping theorems for exponentially bounded C-semigroups in Banach spaces
Let X be a Banach space and C an injective bounded linear operator on X, with dense range. A strongly continuous family \(\{S_ t\}_{t\geq 0}\) of bounded linear operators on X is called an exponentially bounded C- semigroup if (i) \(S_ 0=C;\) (ii) \(S_{s+t}C=S_ sS_ t\) whenever s,t\(\geq 0;\) (iii) \(\| S_ t\| \leq M \exp (at)\) for suitable nonnegative numbers M and a and any \(t\geq 0.\) In the present paper the author proves a spectral mapping theorem for such semigroups.
scientific article; zbMATH DE number 4119043
scientific article