Geodesic
Multipliers and uniformly continuous functionals over Fourier algebras of ultraspherical hypergroups
Filomat, Tome 35 (2021) no. 9, p. 3139

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DOI

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 {u f : 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. 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). We also study the uniformly continuous functionals associated with the Fourier algebra A(H) and obtain some characterizations for H to be discrete. Finally, we establish a contractive and injective representation from Bλ(H) into BσA(H)(Bλ(H)). As an application of this result we show that the induced representation Φ : Bλ(H)→ BσA(H)(Bλ(H)) is surjective if and only if G is amenable
DOI : 10.2298/FIL2109139E
Classification : 43A62, 43A30, 43A22, 46J10
Keywords: Fourier algebras, ultrapherical hypergroups, locally compact groups, multiplier algebras 
Reza Esmailvandi; Mehdi Nemati. Multipliers and uniformly continuous functionals over Fourier algebras of ultraspherical hypergroups. Filomat, Tome 35 (2021) no. 9, p. 3139 . doi: 10.2298/FIL2109139E
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     author = {Reza Esmailvandi and Mehdi Nemati},
     title = {Multipliers and uniformly continuous functionals over {Fourier} algebras of ultraspherical hypergroups},
     journal = {Filomat},
     pages = {3139 },
     year = {2021},
     volume = {35},
     number = {9},
     doi = {10.2298/FIL2109139E},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2109139E/}
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