Multipliers and Uniformly Continuous Functionals Over Fourier Algebras of Ultraspherical Hypergroups
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Title
Multipliers and Uniformly Continuous Functionals Over Fourier Algebras of Ultraspherical HypergroupsDate
2021Publisher
Univerzitet u NisuISSN
0354-5180; 2406-0933Bibliographic citation
ESMAILVANDI, Reza; NEMATI, Mehdi. Multipliers and uniformly continuous functionals over fourier algebras of ultraspherical hypergroups. Filomat, 2021, 35.9: 3139-3150.Type
info:eu-repo/semantics/articleVersion
info:eu-repo/semantics/publishedVersionAbstract
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 ... [+]
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 B
σ
A(H)
(Bλ(H)). As an application of this result we show that the induced representation
Φ : Bλ(H) → B
σ
A(H)
(Bλ(H)) is surjective if and only if G is amenable. [-]
Is part of
Filomat, 2021, 35.9: 3139-3150Rights
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info:eu-repo/semantics/openAccess
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