| Abstract: | We show that several spectral inclusions known for C0-semigroups fail for semigroups of closed operators, even if they can be regularized. We introduce the notion of spectral completeness for the regularizing operator C which implies equality of the spectrum and the C-spectrum of the generator. We prove spectral inclusions under this additional assumption. We give a series of examples in which the regularizing operator is spectrally complete including generators of integrated semigroups, of distribution semigroups, and of some semigroups that are strongly continuous for t > 0. |
