International Journal of Mathematics and Mathematical Sciences
Volume 32 (2002), Issue 10, Pages 635-640
doi:10.1155/S0161171202112221
A note on the spectral operators of scalar type and semigroups of bounded linear
operators
Department of Mathematics and Statistics, Boston University, 111 Cummington Street, Boston 02215, MA, USA
Received 20 December 2001
Copyright © 2002 Marat V. Markin. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
It is shown that, for the spectral operators of scalar type, the well-known characterizations of the generation of C0- 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.