On scalar-type spectral operators and Carleman ultradifferentiable C0-semigroups - Markin, M. V. (Ukrains’kyi Matematychnyi Zhurnal, 2008)
Necessary and sufficient conditions for a scalar-type spectral operator in a Banach space to be a generator of a Carleman ultradifferentiable C0-semigroup are found. The conditions are formulated exclusively in terms of the spectrum of the operator.