Il existe sur des moyennes invariantes et non topologiquement invariantes
A concept of amenability for an arbitrary Lau algebra called inner amenability is introduced and studied. The inner amenability of a discrete semigroup is characterized by the inner amenability of its convolution semigroup algebra. Also, inner amenable Lau algebras are characterized by several equivalent statements which are similar analogues of properties characterizing left amenable Lau algebras.
Let K be an ultraspherical hypergroup associated to a locally compact group G and a spherical projector π and let VN(K) denote the dual of the Fourier algebra A(K) corresponding to K. In this note, invariant means on VN(K) are defined and studied. We show that the set of invariant means on VN(K) is nonempty. Also, we prove that, if H is an open subhypergroup of K, then the number of invariant means on VN(H) is equal to the number of invariant means on VN(K). We also show that a unique topological...