On Exponential Stability of C Semigroups*

In this note, the exponential stability for C0 semigroups in a Hilbert space is considered. First, an expression for a C0 semigroup is given, and then a formula on the growth order of a C0 semigroup is obtained. Finally, with some additional condition such as the boundedness of the resolvent of the generator of a C0 semigroup on an imaginary axis, the exponential stability of a C0 semigroup is proved.