Problems Concerning n-Weak Amenability of a Banach Algebra

Medghalchi, Alireza; Yazdanpanah, T.

doi:10.1007/s10587-005-0071-4

“…It was shown in [4,11] that the n−weak amenability of A ′′ implies the n−weak amenability of A. In [13] it was shown that if the Banach algebra A is complete Arens regular and every derivation D : A → A ′ is weakly compact, the weak amenability of A (2n) for some n ≥ 1 implies of A. The authors in [5,10] determined the conditions that the 3−weak amenability of A ′′ implies the 3−weak amenability of A, and the 3−weak amenability of A (2n) for some (n ≥ 1) implies the 3−weak amenability of A.…”

Section: And Ementioning

confidence: 99%

m−WEAK AMENABILITY OF (2n)−TH DUALS OF BANACH ALGEBRAS

Ettefagh¹

2019

FU Math Inform

0

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“…under the usual matrix operations and l 1 -norm, where A and B are Banach algebras and M is a Banach (A, B)-bimodule. In [16], it is proven that if M 0, then Tri(A, M, B) is not amenable, and hence if M = 0 then Tri(A, M, B) is amenable if and only if A and B are amenable. Let K = 0 M 0 0 , then K is a closed ideal in Tri(A, M, B) and Tri(A, M, B)/K A ⊕ B (isometric isomorphism).…”

Section: Introductionmentioning

confidence: 99%

Relative amenability of Banach algebras

Ghahramani

¹

,

Khodakarami

²

,

Feizi

³

2022

Filomat

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Let A be a Banach algebra and I be a closed ideal of A. We say that A is amenable relative to I, if A/I is an amenable Banach algebra. We study the relative amenability of Banach algebras and investigate the relative amenability of triangular Banach algebras and Banach algebras associated to locally compact groups. We generalize some of the previous known results by applying the concept of relative amenability of Banach algebras, especially, we present a generalization of Johnson?s theorem in the concept of relative amenability.

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“…under the usual matrix operations and l 1 -norm, where A and B are Banach algebras and M is a Banach (A, B)-bimodule. In [16], it is proven that if M = 0, then T ri(A, M, B) is not amenable, and hence if M = 0 then T ri(A, M, B) is amenable if and only if A and B are amenable. Let K = 0 M 0 0 , then K is a closed ideal in T ri(A, M, B) and T ri(A, M, B)/K ∼ = A ⊕ B (isometric isomorphism).…”

Section: Introductionmentioning

confidence: 99%

Approximate semi-amenability of Banach algebras

Ghahramani

¹

,

Loy

²

2020

Semigroup Forum

1

0

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Let A be a Banach algebra and I be a closed ideal of A. We say that A is amenable relative to I, if A/I is an amenable Banach algebra. We study the relative amenability of Banach algebras and investigate the relative amenability of triangular Banach algebras and Banach algebras associated to locally compact groups. We generalize some of the previous known results by applying the concept of relative amenability of Banach algebras, especially, we present a generalization of Johnson's theorem in the concept of relative amenability.

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Problems Concerning n-Weak Amenability of a Banach Algebra

Cited by 4 publications

References 9 publications

m−WEAK AMENABILITY OF (2n)−TH DUALS OF BANACH ALGEBRAS

m−WEAK AMENABILITY OF (2n)−TH DUALS OF BANACH ALGEBRAS

Relative amenability of Banach algebras

Approximate semi-amenability of Banach algebras

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