Character Connes amenability of dual Banach algebras

Ramezanpour, Mohammad

doi:10.21136/cmj.2018.0451-16

Cited by 5 publications

(2 citation statements)

References 24 publications

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“…The notion of ϕ-Connes amenability for a dual Banach algebra A introduced by Mahmoodi and some characterizations were given [8] and [9], where ϕ is a wk * -continuous character on A. We say that A is ϕ-Connes amenable if there exists a bounded linear functional m on σwc(A * ) satisfying m(ϕ) = 1 and m( f • a) = ϕ(a)m( f ) for every a ∈ A and f ∈ σwc(A * ).…”

Section: Remark 22mentioning

confidence: 99%

Johnson pseudo-Connes amenability of dual Banach algebras

Sahami

Shariati

Pourabbas

2021

Filomat

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We introduce the notion of Johnson pseudo-Connes amenability for dual Banach algebras. We study the relation between this new notion with the various notions of Connes amenability like Connes amenability, approximate Connes amenability and pseudo Connes amenability. We also investigate some hereditary properties of this new notion. We prove that for a locally compact group G,M(G) is Johnson pseudo-Connes amenable if and only if G is amenable. Also we show that for every non-empty set I,MI(C) under this new notion is forced to have a finite index. Finally, we provide some examples of certain dual Banach algebras and we study their Johnson pseudo-Connes amenability.

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Section: Remark 22mentioning

confidence: 99%

Johnson pseudo-Connes amenability of dual Banach algebras

Sahami

Shariati

Pourabbas

2021

Filomat

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“…The notion of ϕ-Connes amenability for a dual Banach algebra A introduced by Mahmoodi and some characterizations were given [7] and [8], where ϕ is a wk * -continuous character on A. We say that A is ϕ-Connes amenable if there exists a bounded linear functional m on σwc(A * ) satisfying m(ϕ) = 1 and m(f • a) = ϕ(a)m(f ) for every a ∈ A and f ∈ σwc(A * ).…”

Section: Johnson Pseudo-connes Amenabilitymentioning

confidence: 99%

Johnson pseudo-Connes amenability of dual Banach algebras

Shariati¹,

Pourabbas²,

Sahami³

2018

Preprint

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We introduce the notion of Johnson pseudo-Connes amenability for dual Banach algebras. We study the relation between this new notion with the various notions of Connes amenability like Connes amenability, approximate Connes amenability and pseudo Connes amenability. We also investigate some hereditary properties of this new notion. We prove that for a locally compact group G, M (G) is Johnson pseudo-Connes amenable if and only if G is amenable. Also we show that for every non-empty set I, M I (C) under this new notion is forced to have a finite index. Finally, we provide some examples of certain dual Banach algebras and we study their Johnson pseudo-Connes amenability.

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Approximate Connes-biprojectivity of dual Banach algebras

Sahami

Shariati

Pourabbas

2020

Asian-European J. Math.

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In this paper, we introduce a notion of approximate Connes-biprojectivity for dual Banach algebras. We study the relation between approximate Connes-biprojectivity, approximate Connes amenability and [Formula: see text]-Connes amenability. We propose a criterion to show that certain dual triangular Banach algebras are not approximately Connes-biprojective. Next, we show that for a locally compact group [Formula: see text], the Banach algebra [Formula: see text] is approximately Connes-biprojective if and only if [Formula: see text] is amenable. Finally, for an infinite commutative compact group [Formula: see text], we show that the Banach algebra [Formula: see text] with convolution product is approximately Connes-biprojective, but it is not Connes-biprojective.

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Character Connes amenability of dual Banach algebras

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Cited by 5 publications

References 24 publications

Johnson pseudo-Connes amenability of dual Banach algebras

Johnson pseudo-Connes amenability of dual Banach algebras

Johnson pseudo-Connes amenability of dual Banach algebras

Approximate Connes-biprojectivity of dual Banach algebras

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