2019/05/09 by Reza Esmailvandi, Esmailvandi, Reza, Mehdi Nemati +1
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Holomorphic and Operator Theory
paper · pdf · doi:10.48550/arxiv.1905.03569
Let H be an ultraspherical hypergroup associated to a locally compact group G and let A(H) be the Fourier algebra of H. For a left Banach A(H)-submodule X of VN(H), define QX to be the norm closure of the linear span of the set \uf: u∈ A(H), f∈ X\ in BA(H)(A(H), X^*)^*. We will show that BA(H)(A(H), X^*) is a dual Banach space with predual QX, we characterize QX in terms of elements in A(H) and X. Applications obtained on the multiplier algebra M(A(H)) of the Fourier algebra A(H). In particular, we prove that G is amenable if and only if M(A(H))= Bλ(H), where Bλ(H) is the reduced Fourier-Stieltjes algebra of H . Finally, we investigate some characterizations for an ultraspherical hypergroup to be discrete.