The closeness and closability criteria for infinitesimal operators of certain semigroups (Q647897)

There are considered a Banach space \(X\), the Banach space of its endomorphism \(\text{End} X\), the semigroup \(T: (0,\infty)\rightarrow \text{End} X\), and the infinitesimal operator \(A_0\) of the semigroup \(T\). The author obtains necessary and sufficient conditions for the non-closability of operator \(A_0\) in the operator class and also necessary and sufficient conditions for the closedness of \(A_0\). Some examples of closed and non-closeable infinitesimal operators are studied.