ZL-amenability and characters for the restricted direct products of finite groups

Alaghmandan, Mahmood; Choi, Yemon; Samei, Ebrahim

doi:10.1016/j.jmaa.2013.09.030

Cited by 4 publications

(11 citation statements)

References 15 publications

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“…Here we note that Lemma 2.1 generalizes former known results for compact and discrete cases in [2] and [1]. Now we consider the weighted case.…”

Section: Central Beurling Algebras On [Fc] − Groupssupporting

confidence: 71%

“…So investigation of weak amenability for ZL 1 (G, ω) is a natural extension of the study for the commutative groups. We notice that some investigations on amenability and weak amenability of ZL 1 (G), the case with the trivial weight ω = 1, have been made recently in [2] and [1]. All theses studies even for amenability have answers only for particular cases of locally compact groups, in particular the ones in [2] and [1] are only on compact and some discrete groups.…”

Section: Introductionmentioning

confidence: 99%

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Weak amenability of the central Beurling algebras on [FC]- groups

Shepelska¹,

Zhang²

2017

Michigan Math. J.

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We study weak amenability of central Beurling algebras ZL 1 (G, ω). The investigation is a natural extension of the known work on the commutative Beurling algebra L 1 (G, ω). For [FC] − groups we establish a necessary condition and for [FD] − groups we give sufficient conditions for the weak amenability of ZL 1 (G, ω). For a compactly generated [FC] − group with the polynomial weight ωα(x) = (1 + |x|) α , we prove that ZL 1 (G, ωα) is weakly amenable if and only if α < 1/2.

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“…Here we note that Lemma 2.1 generalizes former known results for compact and discrete cases in [2] and [1]. Now we consider the weighted case.…”

Section: Central Beurling Algebras On [Fc] − Groupssupporting

confidence: 71%

Section: Introductionmentioning

confidence: 99%

Weak amenability of the central Beurling algebras on [FC]- groups

Shepelska¹,

Zhang²

2017

Michigan Math. J.

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“…Also for a specific class of FC groups, called RDPF groups, the amenability of Z 1 (G) is characterized in [5]. The main result of [5] for a RDPF group G is, Z 1 (G) is amenable if and only if |G | < ∞. These two studies suggest that the later characterization for RDPF groups may be extendible to general FC groups.…”

Section: Za(g) Of Compact Groupsmentioning

confidence: 99%

“…Remark Recall that in , it was proved that for a locally compact group G with a finite derived subgroup

G^{'}, Z L^{1} false(G false)

is amenable. Also for a specific class of FC groups, called RDPF groups, the amenability of

Z ℓ^{1} false(G false)

is characterized in . The main result of for a RDPF group G is,

Z ℓ^{1} false(G false)

is amenable if and only if

false| G^{'} false| < \infty

.…”

Section: Amenability Of Hypergroup Algebrasmentioning

confidence: 99%

Amenability notions of hypergroups and some applications to locally compact groups

Alaghmandan

2017

Math. Nachr.

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Different notions of amenability on hypergroups and their relations are studied. Developing Leptin's theorem for discrete hypergroups, we characterize the existence of a bounded approximate identity for hypergroup Fourier algebras. We study the Leptin condition for discrete hypergroups derived from the representation theory of some classes of compact groups. Studying amenability of the hypergroup algebras for discrete commutative hypergroups, we obtain some results on amenability properties of some central Banach algebras on compact and discrete groups.Keyword: hypergroups; Fourier algebra; amenability; compact groups; finite conjugacy groups.AMS codes: 43A62, 46H20.In this paper, we investigate different amenability notions of hypergroups and their relations. In particular, we look closer at a generalization of Følner type conditions over hypergroups. This generalization lets us to investigate more structural properties of some classes of hypergroups. In particular we study the existence of bounded approximate identities for the Fourier algebra of regular Fourier hypergroups. We prove a hypergroup analogue of Leptin's theorem for discrete regular Fourier hypergroups that is, the existence of a bounded approximate identity for the Fourier algebra is equivalent to the existence of a square integrable Reiter's net. The later condition is denoted by (P 2 ).We also study amenability of hypergroup algebras (as Banach algebras) for discrete commutative hypergroups satisfying (P 2 ). We show that for this class of hypergroups, the hypergroup algebra cannot be amenable if the inverse of the Haar measure vanishes at infinity. This result and the appearance of (P 2 ) in hypergroup Leptin's theorem emphasize the importance of the amenability notion (P 2 ). At the end we apply these results to some examples of hypergroup structures which are admitted by two classes of locally compact groups, namely compact and discrete groups.1

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“…Note that [18] generalizes the results of [1,2] and in these three articles the major focus was on studying the amenability and weak amenability properties. The idea behind the proofs given in [18,2] is to use a projection from L 1 (G) onto Z(L 1 (G)).…”

Section: Introductionmentioning

confidence: 78%

Center of Banach algebra valued Beurling algebras

Talwar,

Jain

2021

Preprint

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ZL-amenability and characters for the restricted direct products of finite groups

Cited by 4 publications

References 15 publications

Weak amenability of the central Beurling algebras on [FC]- groups

Weak amenability of the central Beurling algebras on [FC]- groups

Amenability notions of hypergroups and some applications to locally compact groups

Center of Banach algebra valued Beurling algebras

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