Compact and Weakly Compact Multipliers on Fourier Algebras of Ultraspherical Hypergroups

Esmailvandi, Reza; Nemati, Mehdi

doi:10.1007/s00009-020-01651-y

Cited by 3 publications

(7 citation statements)

References 21 publications

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“…Let H be an ultraspherical hypergroup associated with a locally compact group G and a spherical projector Let denote the Fourier algebra corresponding to the ultraspherical hypergroup Also, let denote the hypergroup von Neumann algebra of The algebra although introduced a decade ago, has not received much attention. For some of the recent contributions to , see for example, [7, 10, 11, 23]. This paper is a continuation of the series of results obtained by the first and the second authors.…”

Section: Introductionmentioning

confidence: 75%

“…If is discrete, then is an ideal in by [11, Proposition ]. Hence, the result follows from Theorem 5.6.…”

Section: Unit Elementsmentioning

confidence: 94%

“…The notion of weakly almost periodic functionals and uniformly continuous functionals on has been studied in a recent paper [11]. In Section 3 of this paper, we show that the space of all uniformly continuous functionals forms a C*-algebra.…”

Section: Introductionmentioning

confidence: 95%

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On the Algebras and of an Ultraspherical Hypergroup

Esmailvandi

Nemati²,

Kumar

2022

J. Aust. Math. Soc.

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Let H be an ultraspherical hypergroup and let $A(H)$ be the Fourier algebra associated with $H.$ In this paper, we study the dual and the double dual of $A(H).$ We prove among other things that the subspace of all uniformly continuous functionals on $A(H)$ forms a $C^*$ -algebra. We also prove that the double dual $A(H)^{\ast \ast }$ is neither commutative nor semisimple with respect to the Arens product, unless the underlying hypergroup H is finite. Finally, we study the unit elements of $A(H)^{\ast \ast }.$

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Section: Introductionmentioning

confidence: 75%

“…If is discrete, then is an ideal in by [11, Proposition ]. Hence, the result follows from Theorem 5.6.…”

Section: Unit Elementsmentioning

confidence: 94%

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On the Algebras and of an Ultraspherical Hypergroup

Esmailvandi

Nemati²,

Kumar

2022

J. Aust. Math. Soc.

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“…Taking the infimum over all possible choices of V and W in the representation (11) of , we obtain that F m ≤ cb . (ii) Let F ∈ S(A, G, α).…”

Section: Proposition 32 Let G Be a Non-discrete Locally Compact Group...mentioning

confidence: 99%

“…In [22], Lau showed that the Fourier algebra A(G) has a non-zero weakly compact left multiplier if and only if G is discrete and that, for discrete amenable groups, A(G) coincides with the algebra of its weakly compact multipliers. We refer the reader to [7,11,15] for further related results.…”

Section: Introductionmentioning

confidence: 99%

Completely Compact Herz–Schur Multipliers of Dynamical Systems

Todorov

Turowska

2022

J Fourier Anal Appl

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We prove that if G is a discrete group and $$(A,G,\alpha )$$ ( A , G , α ) is a C*-dynamical system such that the reduced crossed product $$A\rtimes _{r,\alpha } G$$ A ⋊ r , α G possesses property (SOAP) then every completely compact Herz–Schur $$(A,G,\alpha )$$ ( A , G , α ) -multiplier can be approximated in the completely bounded norm by Herz–Schur $$(A,G,\alpha )$$ ( A , G , α ) -multipliers of finite rank. As a consequence, if G has the approximation property (AP) then the completely compact Herz–Schur multipliers of A(G) coincide with the closure of A(G) in the completely bounded multiplier norm. We study the class of invariant completely compact Herz–Schur multipliers of $$A\rtimes _{r,\alpha } G$$ A ⋊ r , α G and provide a description of this class in the case of the irrational rotation algebra.

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Characterization of Weakly Compact Multipliers on Left $$\phi $$-Amenable Banach Algebras

Soltani Renani,

Yari

2023

Vietnam J. Math.

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Compact and Weakly Compact Multipliers on Fourier Algebras of Ultraspherical Hypergroups

Cited by 3 publications

References 21 publications

On the Algebras and of an Ultraspherical Hypergroup

On the Algebras and of an Ultraspherical Hypergroup

Completely Compact Herz–Schur Multipliers of Dynamical Systems

Characterization of Weakly Compact Multipliers on Left $$\phi $$-Amenable Banach Algebras

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