On the actions of a locally compact group on some of its semigroup compactifications

• Autores: M. Filali
• Localización: Mathematical proceedings of the Cambridge Philosophical Society, ISSN 0305-0041, Vol. 143, Nº 1, 2007, págs. 25-39
• Idioma: inglés
• DOI: 10.1017/s0305004107000242
• Texto completo no disponible (Saber más ...)
• Resumen

  • Let G be a locally compact group and be its largest semigroup compactification. Then sx?x in whenever s is an element in G other than e. This result was proved by Ellis in 1960 for the case G discrete (and so is the Stone¿Cech compactification ßG of G), and by Veech in 1977 for any locally compact group. We study this property in the WAP ¿ compactification of G; and in , we look at the situation when xs?x. The points are separated by some weakly almost periodic functions which we are able to construct on a class of locally compact groups, which includes the so-called E-groups introduced by C. Chou and which is much larger than the class of SIN groups. The other consequences deduced with these functions are: a generalization of some theorems on the regularity of due to Ruppert and Bouziad, an analogue in of the ¿local structure theorem¿ proved by J. Pym in , and an improvement of some earlier results proved by the author and J. Baker on .