Compact and Weakly Compact Multipliers on Fourier Algebras of Ultraspherical Hypergroups.

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). [ABSTRACT FROM AUTHOR]