Geodesic
Semidirect Product Compactifications
Canadian journal of mathematics, Tome 35 (1983) no. 1, pp. 1-32

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

1. Introduction. K. Deleeuw and I. Glicksberg [4] proved that if S and T are commutative topological semigroups with identity, then the Bochner almost periodic compactification of S × T is the direct product of the Bochner almost periodic compactifications of S and T. In Section 3 we consider the semidirect product of two semi topological semigroups with identity and two unital C*-subalgebras and of W(S) and W(T) respectively, where W(S) is the weakly almost periodic functions on S. We obtain necessary and sufficient conditions and for a semidirect product compactification of to exist such that this compactification is a semi topological semigroup and such that this compactification is a topological semigroup. Moreover, we obtain the largest such compactifications. 
Dangello, F.; Lindahl, R. Semidirect Product Compactifications. Canadian journal of mathematics, Tome 35 (1983) no. 1, pp. 1-32. doi: 10.4153/CJM-1983-001-7
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[1] 1. Berglund, J. F., Junghenn, H. D. and Milnes, P., Compact right topological semigroups and generalizations of almost periodicity (Springer-Verlag, New York, 1978). Google Scholar

[2] 2. Berglund, J. F. and Milnes, P., Algebras of functions on semi-topological left-groups, Trans. Amer. Math. Soc. 222 (1976), 157–178. Google Scholar

[3] 3. Burckel, R. B., Weakly almost periodic functions on semigroups (Gordon and Breach, New York, 1970). Google Scholar

[4] 4. Deleeuw, K. and Glicksberg, I., Almost periodic functions on semigroups, Acta Math. 105 (1961), 99–140. Google Scholar

[5] 5. Deleeuw, K. and Glicksberg, I., Applications of almost periodic compactifications, Acta Math. 105 (1961), 63–97. Google Scholar

[6] 6. Edwards, R., Functional analysis (Holt, Rinehart, and Winston, New York, 1965). Google Scholar

[7] 7. Ellis, R., Locally compact transformation groups, Duke Math. J. 24 (1957), 119–125. Google Scholar

[8] 8. Grothendieck, A., Critères de compacité dans les espaces fonctionnels généraux, Amer. J. Math. 74 (1952), 168–186. Google Scholar

[9] 9. Hewitt, E. and Ross, K. A., Abstract harmonie analysis I (Academic Press, New York, 1963). Google Scholar

[10] 10. Junghenn, H. D., Almost periodic compactifications of transformation semigroups, Pacific J. Math. 57 (1975), 207–216. Google Scholar

[11] 11. Junghenn, H. D., Almost periodic functions on semidirect products of transformation semigroups, Pacific J. Math. 79 (1978), 117–128. Google Scholar

[12] 12. Junghenn, H. D., C*-algebras of functions on direct products of semigroups, Rocky Mountain J. Math. 10 (1980), 589–597. Google Scholar

[13] 13. Junghenn, H. D., Tensor products of spaces of almost periodic functions, Duke Math J. 41 (1974), 661–666. Google Scholar

[14] 14. Junghenn, H. D. and Lerner, B. T., Semigroup compactifications of semidirect products, Trans. Amer. Math. Soc. 265 (1981), 393–404. Google Scholar

[15] 15. Landstad, M., On the Bohr compactification of a transformation group, Math. Zeit. 127 (1972), 167–178. Google Scholar

[16] 16. Milnes, P., Semigroup compactifications of direct and semidirect products, Preprint. Google Scholar

[17] 17. Mitchell, T., Function algebras, means, and fixed points, Trans. Amer. Math. Soc. 130 (1968), 117–126. Google Scholar

[18] 18. Rickart, C. R., General theory of Banach algebras (D. Van Nostrand, Princeton, N.J., 1960). Google Scholar

[19] 19. Schatten, R., A theory of cross-spaces (Ann. of Math. Studies, Princeton University Press, Princeton, N.J., 1950). Google Scholar

[20] 20. Troallic, J.-P., Fonctions à valeurs dans des espaces fonctionnels généraux: théorèmes de R. Ellis et de I. Namioka, C. R. Acad. Se. Paris 287 (1978), 63–66. Google Scholar

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