The coincidence of some topologies on the unit ball of the Fourier - Stieltjes algebra of weighted foundation semigroups
Bami, M. Lashkarizadeh
Bull. Belg. Math. Soc. Simon Stevin, Tome 11 (2005) no. 5, p. 535-542 / Harvested from Project Euclid
In our earlier paper [{\bf 10}], for a foundation $*-$semigroup $S$ with an identity and with a Borel-measurable weight function $w\leq 1$, we proved that on the unit ball of ${\cal P} (S,w)$, the cone of $w-$bounded continuous positive definite functions on $S$, the weak topology coincides with the compact open topology. In the present paper, through some $C^*-$algebras techniques, we shall extend this result to the unit ball of the Fourier-Stieltjes algebra ${\cal F} (S,w)$ of a foundation semigroup $S$ with a Borel measurable weight function $w$. Indeed, we shall establish our conjecture in [{\bf 10}] even in the more general setting of the Fourier-Stieltjes algebra ${\cal F}(S,w)$ for any Borel measurable weight function $w$. It should be noted that the family of foundation semigroups is quite extensive, for which locally compact groups and discrete semigroups are elementary examples. For further examples we refer to Appendix B of [{\bf 13}].
Publié le : 2005-12-14
Classification: 
@article{1133793341,
     author = {Bami, M. Lashkarizadeh},
     title = {The coincidence of some topologies on the unit ball of the 
 Fourier - Stieltjes algebra of weighted foundation semigroups},
     journal = {Bull. Belg. Math. Soc. Simon Stevin},
     volume = {11},
     number = {5},
     year = {2005},
     pages = { 535-542},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1133793341}
}
Bami, M. Lashkarizadeh. The coincidence of some topologies on the unit ball of the 
 Fourier - Stieltjes algebra of weighted foundation semigroups. Bull. Belg. Math. Soc. Simon Stevin, Tome 11 (2005) no. 5, pp.  535-542. http://gdmltest.u-ga.fr/item/1133793341/