Weighted discrete hypergroups. (English) Zbl 1342.43006
Summary: Weighted group algebras have been studied extensively in abstract harmonic analysis, where complete characterizations have been found for some important properties of weighted group algebras, namely, amenability and Arens regularity. One of the generalizations of weighted group algebras is weighted hypergroup algebras. Defining weighted hypergroups, analogous to weighted groups, we study Arens regularity and isomorphism to operator algebras for them. We also examine our results on three classes of discrete weighted hypergroups constructed by conjugacy classes of FC groups, the dual space of compact groups, and the hypergroup structure defined by orthogonal polynomials. We observe some unexpected examples regarding Arens regularity and operator isomorphisms of weighted hypergroup algebras.
MSC:
43A62 | Harmonic analysis on hypergroups |
43A77 | Harmonic analysis on general compact groups |
43A30 | Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc. |
20F24 | FC-groups and their generalizations |