Compact and weakly compact multipliers on Fourier algebras of ultraspherical hypergroups

Esmailvandi, Reza; Nemati, Mehdi

doi:10.48550/arxiv.1907.03584

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2021

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“…acknowledges the support and hospitality at Queen's University Belfast during several visits in 2018 and 2019. amenable groups, A(G) coincides with the algebra of its weakly compact multipliers. We refer the reader to [17], [12] and [7] for further related results.…”

Section: Introductionmentioning

confidence: 99%

Completely compact Herz-Schur multipliers of dynamical systems

He¹,

Todorov²,

Turowska³

2021

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We prove that if G is a discrete group and (A, G, α) is a C*-dynamical system such that the reduced crossed product A ⋊r,α G possesses property (SOAP) then every completely compact Herz-Schur (A, G, α)-multiplier can be approximated in the completely bounded norm by Herz-Schur (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 ⋊r,α G and provide a description of this class in the case of the irrational rotation algebra.

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Section: Introductionmentioning

confidence: 99%