Geodesic
Semigroup Compactifications of Direct and Semidirect Products
Canadian mathematical bulletin, Tome 26 (1983) no. 2, pp. 233-240

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

A classical result of I. Glicksberg and K. de Leeuw asserts that the almost periodic compactification of a direct product S × T of abelian semigroups with identity is (canonically isomorphic to) the direct product of the almost periodic compactiflcations of S and T. Some efforts have been made to generalize this result and recently H. D. Junghenn and B. T. Lerner have proved a theorem giving necessary and sufficient conditions for an F-compactification of a semidirect product S⊗σ T to be a semidirect product of compactiflcations of S and T. A different such theorem is presented here along with a number of corollaries and examples which illustrate its scope and limitations. Some behaviour that can occur for semidirect products, but not for direct products, is exposed
DOI : 10.4153/CMB-1983-037-2
Mots-clés : 22A15, 22A20, 43A60, semitopological semigroup, (semidirect) product, (right topological) compactification 
Milnes, Paul. Semigroup Compactifications of Direct and Semidirect Products. Canadian mathematical bulletin, Tome 26 (1983) no. 2, pp. 233-240. doi: 10.4153/CMB-1983-037-2
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[1] 1. Berglund, J. F., Junghenn, H. D. and Milnes, P., Compact right topological semigroups and generalizations of almost periodicity, Lecture Notes in Mathematics, Vol. 663, Springer-Verlag, Berlin, 1978. Google Scholar

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

[3] 3. Chou, C., Weakly almost periodic functions and Fourier-Stieltjes algebras of locally compact groups. Google Scholar

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

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

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

[7] 7. Junghenn, H. D., Distal compactifications of semigroups. Google Scholar

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

[9] 9. Milnes, P., Continuity properties of compact right topological groups, Proc. Camb. Phil. Soc. 86 (1979), 427–435. Google Scholar

[10] 10. Milnes, P., Almost periodic compactifications of direct and semidirect products Coll. Math. 44 (1981) 125–136. Google Scholar

[11] 11. Veech, W. A., Weakly almost periodic functions on semisimple Lie groups, Mona. Math. 88 (1979), 55–68. Google Scholar

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