Characteristic Conditions of the Generation of C Semigroups in a Hilbert Space1

In this paper new characteristic conditions, in terms of A and the first order resolvent of A and A*, which assure that A generates a C0 semigroup in a Hilbert space are proposed and proved. The conditions can be used to investigate the well-posedness problem of non-dissipative systems. An example is also given to show how to use them