A note on two equivalence relations on inverse semigroups

“…the quotient S/≈ is a discrete group (see also [2]). Indeed, S/≈ is homomorphic to the maximal group homomorphic image G S [19] of S [21]. Moreover, S is amenable if and only if G S = S/≈ is amenable [9,19].…”

Section: Theorem Let a Be A Banach A-module Such That A⊗ A A Is A Comentioning

confidence: 99%

“…It is shown in [2] that C/ ≈ is isomorphic to the group of integers Z, hence C is amenable (see also [9] and [21]). Therefore, by Theorem 3.13, ℓ 1 (C) is module pseudo-amenable as an ℓ 1 (E C )-module but ℓ 1 (C) * * is not.…”

Section: 14mentioning

confidence: 99%

“…We consider an equivalence relation on S such that s ≈ t if and only if δ s − δ t ∈ J for all s, t ∈ S. It is shown in [20] that the quotient S/≈ is a discrete group (see also [2]). Indeed, S/≈ is homomorphic to the maximal group homomorphic image G S [19] of S [21]. Moreover, S is amenable if and only if G S = S/≈ is amenable [9,19].…”

Section: Theorem Let a Be A Banach A-bimodule With Compatible Actions...mentioning

confidence: 99%

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n-Weak Module Amenability of Triangular Banach Algebras

Bodaghi

Jabbari²

2015

Mathematica Slovaca

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Let A, B be Banach A-modules with compatible actions and M be a left Banach A-A-module and a right Banach B-A-module. In the current paper, we study module amenability, n-weak module amenability and module Arens regularity of the triangular Banach algebra T = A M B (as an T :=. We employ these results to prove that for an inverse semigroup S with subsemigroup E of idempotents, the triangular Banachis permanently weakly module amenable (as an T 0 = 1 (E) 1 (E) -module). As an example, we show that T 0 is T 0 -module Arens regular if and only if the maximal group homomorphic image G S of S is finite.

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“…Then the quotient S/ ≈ is a discrete group (see [4,20]), and it is isomorphic to the maximal group homomorphic image G S of S (see [19]). As in [21,Theorem 3.3], we may observe that l 1 (S)/J ∼ = l 1 (S/ ≈).…”

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confidence: 99%

A generalization of the $$n$$ n -weak module amenability of banach algebras

Arslan

Inceboz

2014

Semigroup Forum

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In this paper, we generalize the notion of n-weak module amenability of a Banach algebra A which is a Banach module over another Banach algebra U with compatible actions to that of (σ ) − n-weak module amenability for n ∈ N and σ ∈ Hom U (A). We also investigate the relation between this new concept of amenability of A and the quotient Banach algebra A/J where J is the closed ideal of A generated by elements of the form (a · α)b − a(α · b) for a, b ∈ A and α ∈ U . As a consequence, we show that the semigroup algebra l 1 (S) is (σ )-(2n + 1)-weakly module amenable as an l 1 (E)-module for each n ∈ N and σ ∈ Hom l 1 (E) (l 1 (S)), where S is an inverse semigroup with the set of idempotents E.

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A note on two equivalence relations on inverse semigroups

Cited by 12 publications

References 4 publications

Module character inner amenability of Banach algebras

Module character inner amenability of Banach algebras

n-Weak Module Amenability of Triangular Banach Algebras

A generalization of the $$n$$ n -weak module amenability of banach algebras

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