A note on the spectral operators of scalar type and semigroups of bounded linear operators (Q1854178)

Summary: It is shown that, for the spectral operators of scalar type, the well-known characterizations of the generation of \(C_{0}\)- and analytic semigroups of bounded linear operators can be reformulated exclusively in terms of the spectrum of such operators, the conditions on the resolvent of the generator being automatically met and the corresponding semigroup being that of the exponentials of the operator.