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Semigroups of Operators in C(S)

Published online by Cambridge University Press:  20 November 2018

F. Dennis Sentilles
F. Dennis Sentilles*
Affiliation:
University of Missouri, Columbia, Missouri
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Our study in this paper is two-fold: One is that of a semigroup of linear operators on the space C(S) of bounded continuous functions on a locally compact Hausdorff space S, while the other is that of a transition function of measures in the Banach space M(S) of bounded regular Borel measures on S. It will be seen that an informative and essentially non-restrictive theory of the former can be obtained when C(S) is given the strict topology rather than the usual supremum norm topology and that, in this setting, the natural relationship between semigroups and transition functions obtained when S is compact is maintained, essentially because the dual of C(S) with the strict topology is M(S).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 22 , Issue 1 , 01 February 1970 , pp. 47 - 54
Copyright
Copyright © Canadian Mathematical Society 1970

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