2019/07/08 by Esmailvandi, Reza, Nemati, Mehdi
#43A22 #43A30 #43A62 #46J10 #46J20 #FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.1907.03584
A locally compact group G is discrete if and only if the Fourier algebra A(G) has a non-zero (weakly) compact multiplier. We partially extend this result to the setting of ultraspherical hypergroups. Let H be an ultraspherical hypergroup and let A(H) denote the corresponding Fourier algebra. We will give several characterizations of discreteness of H in the terms of the algebraic properties of A(H). We also study Arens regularity of closed ideals of A(H).