Arens regularity of module actions

Gordji, M. Eshaghi; Filali, M.

doi:10.4064/sm181-3-3

Cited by 24 publications

(20 citation statements)

References 20 publications

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“…We can also prove Theorem 2.4 by applying Corollary 2.1. In fact, the conditions imposed on A imply that A is Arens regular (see [12,Theorem 4.3]). Furthermore, it is not difficult to check in this case that every derivation D : A → A * satisfies D ′′ (A * * ) ⊆ A * .…”

Section: This Is True If and Only If For Everymentioning

confidence: 99%

Weak amenability of the second dual of a Banach algebra

Gordji

Filali

2007

Studia Math.

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Section: This Is True If and Only If For Everymentioning

confidence: 99%

Weak amenability of the second dual of a Banach algebra

Gordji

Filali

2007

Studia Math.

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“…Let us recall from [10] that the topological centres of the left and right module actions of A (2) on A (2) are as follows:…”

Section: Corollary 36 Suppose That Eithermentioning

confidence: 99%

Amalgamated duplication of the Banach algebra 𝔄 along a 𝔄-bimodule 𝒜

Javanshiri

Nemati

2018

J. Algebra Appl.

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Let A and A be Banach algebras such that A is a Banach A-bimodule with compatible actions. We define the product A ⋊ A, which is a strongly splitting Banach algebra extension of A by A. After characterization of the multiplier algebra, topological centre, (maximal) ideals and spectrum of A ⋊ A, we restrict our investigation to the study of semisimplicity, regularity, Arens regularity of A ⋊ A in relation to that of the algebras A, A and the action of A on A. We also compute the first cohomology group H 1 (A ⋊ A, (A ⋊ A) (n) ) for all n ∈ N ∪ {0} as well as the first-order cyclic cohomology group H 1 λ (A ⋊ A, (A ⋊ A) (1) ), where (A ⋊ A) (n) is the n-th dual space of A ⋊ A when n ∈ N and A ⋊ A itself when n = 0. These results are not only of interest in their own right, but also they pave the way for obtaining some new results for Lau products and module extensions of Banach algebras as well as triangular Banach algebra. Finally, special attention is devoted to the cyclic and n-weak amenability of A ⋊ A.Mathematics Subject Classification (2010). 46H20, 46H25, 46H10, 47B48, 47B47, 16E40.

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“…(i) If θ = 0, then [11]) Let S = A ⊕ X be the module extension Banach algebra corresponding A and X.…”

Section: Topological Centresmentioning

confidence: 99%

On amalgamated Banach algebras

Aghababa

Shirmohammadi

2016

Period Math Hung

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Abstract. Let A and B be Banach algebras, θ : A → B be a continuous Banach algebra homomorphism and I be a closed ideal in B. Then the direct sum of A and I with respect to θ, denoted A ⊲⊳ θ I, with a special product becomes a Banach algebra which is called the amalgamated Banach algebra. In this paper, among other things, we compute the topological centre of A ⊲⊳ θ I in terms of that of A and I. Using this, we provide a characterization of the Arens regularity of A ⊲⊳ θ I. Then we determine the character space of A ⊲⊳ θ I in terms of that of A and I. Moreover, we study the weak amenability of A ⊲⊳ θ I.

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Arens regularity of module actions

Cited by 24 publications

References 20 publications

Weak amenability of the second dual of a Banach algebra

Weak amenability of the second dual of a Banach algebra

Amalgamated duplication of the Banach algebra 𝔄 along a 𝔄-bimodule 𝒜

On amalgamated Banach algebras

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