Geodesic
Semigroups of Operators in C(S)
Canadian journal of mathematics, Tome 22 (1970) no. 1, pp. 47-54

Voir la notice de l'article provenant de la source Cambridge University Press

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). 
Sentilles, F. Dennis. Semigroups of Operators in C(S). Canadian journal of mathematics, Tome 22 (1970) no. 1, pp. 47-54. doi: 10.4153/CJM-1970-006-8
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[1] 1. Buck, R. C., Bounded continuous junctions on a locally compact space, Michigan Math. J. 5 (1958), 95–104. Google Scholar

[2] 2. Conway, J. B., The strict topology and compactness in the space of measures, Trans. Amer. Math. Soc. 126 (1967), 474–486. Google Scholar

[3] 3. Dorroh, J. R., Semigroups of maps in a locally compact space, Can. J. Math. 19 (1967), 688–696. Google Scholar

[4] 4. Dorroh, J. R., Localization of the strict topology via bounded sets, Proc. Amer. Math. Soc. 20 (1969), 413–414. Google Scholar

[5] 5. Dunford, N. and Schwartz, J. T., Linear operators. I (Interscience, New York, 1958). Google Scholar

[6] 6. Dynkin, E. B., Markov processes (Springer, Berlin, 1961). Google Scholar

[7] 7. Komatsu, H., Semigroups of operators in a locally convex space, J. Math. Soc. Japan 16 (1964), 230–262. Google Scholar

[8] 8. Meyer, P. A., Probability and potentials (Blaisdell, Waltham, Massachusetts, 1966). Google Scholar

[9] 9. Neveu, J., Mathematical foundations of the theory of probability (Holden-Day, San Francisco, 1965). Google Scholar

[10] 10. Sentilles, F. D., Kernel representations of operators and their adjoints, Pacific J. Math. 23 (1967), 153–162. Google Scholar

[11] 11. Singbal-Vedak, K., A note on semigroups of operators on a locally convex space, Proc. Amer. Math. Soc. 16 (1965), 696–702. Google Scholar

[12] 12. Yosida, K., Functional analysis (Springer, Berlin, 1966). Google Scholar

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