Weak Module Amenability for Semigroup Algebras

2005 ◽  
Vol 71 (1) ◽  
pp. 18-26 ◽  
Author(s):  
Massoud Amini ◽  
Davood Ebrahimi Bagha
Keyword(s):  
Semigroup Algebras ◽  
Module Amenability ◽  
Weak Module

The first module (σ,τ)-cohomology group of triangular Banach algebras of order three

2018 ◽  
Vol 17 (12) ◽  
pp. 1850225
Author(s):  
Hülya İnceboz ◽  
Berna Arslan
Keyword(s):  
Semigroup Forum ◽  
Banach Algebra ◽  
Cohomology Group ◽  
Banach Algebras ◽  
Module Structure ◽  
Semigroup Algebras ◽  
Module Amenability ◽  
Weak Module ◽  
Triangular Banach Algebras

The notion of module amenability for a class of Banach algebras, which could be considered as a generalization of Johnson’s amenability, was introduced by Amini in [Module amenability for semigroup algebras, Semigroup Forum 69 (2004) 243–254]. The weak module amenability of the triangular Banach algebra [Formula: see text], where [Formula: see text] and [Formula: see text] are Banach algebras (with [Formula: see text]-module structure) and [Formula: see text] is a Banach [Formula: see text]-module, is studied by Pourabbas and Nasrabadi in [Weak module amenability of triangular Banach algebras, Math. Slovaca 61(6) (2011) 949–958], and they showed that the weak module amenability of [Formula: see text] triangular Banach algebra [Formula: see text] (as an [Formula: see text]-bimodule) is equivalent with the weak module amenability of the corner algebras [Formula: see text] and [Formula: see text] (as Banach [Formula: see text]-bimodules). The main aim of this paper is to investigate the module [Formula: see text]-amenability and weak module [Formula: see text]-amenability of the triangular Banach algebra [Formula: see text] of order three, where [Formula: see text] and [Formula: see text] are [Formula: see text]-module morphisms on [Formula: see text]. Also, we give some results for semigroup algebras.

scholarly journals Permanent Weak Module Amenability of Semigroup Algebras

2015 ◽  
Vol 0 (0) ◽  
Author(s):  
Abasalt Bodaghi ◽  
Massoud Amini ◽  
Ali Jabbari
Keyword(s):  
Inverse Semigroup ◽  
Banach Algebras ◽  
Tensor Products ◽  
Semigroup Algebras ◽  
Left Action ◽  
Module Amenability ◽  
Weak Module ◽  
Projective Tensor

Abstract We employ the fact that L1(G) is n-weakly amenable for each n ≥ 1 to show that for an inverse semigroup S with the set of idempotents E, ℓ1(S) is n- weakly module amenable as an ℓ1(E)-module with trivial left action. We study module amenability and weak module amenability of the module projective tensor products of Banach algebras.

scholarly journals Module amenability of the second dual and module topological center of semigroup algebras

2010 ◽  
Vol 80 (2) ◽  
pp. 302-312 ◽  
Author(s):  
Massoud Amini ◽  
Abasalt Bodaghi ◽  
Davood Ebrahimi Bagha
Keyword(s):  
Semigroup Algebras ◽  
Topological Center ◽  
Module Amenability ◽  
Second Dual

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

2014 ◽  
Vol 91 (3) ◽  
pp. 625-640 ◽  
Author(s):  
Berna Arslan ◽  
Hülya İnceboz
Keyword(s):  
Banach Algebras ◽  
Module Amenability ◽  
Weak Module

scholarly journals Module amenability of restricted semigroup algebras under module actions

Filomat ◽  
2015 ◽  
Vol 29 (4) ◽  
pp. 787-793
Author(s):  
Abbas Sahleh ◽  
Somaye Tanha
Keyword(s):  
Inverse Semigroup ◽  
Semigroup Algebra ◽  
Semigroup Algebras ◽  
Clifford Semigroup ◽  
Module Amenability

In this article, weshow that module amenability with the canonical action of restricted semigroup algebra l1r (S) and semigroup algebra l1(Sr) are equivalent, where Sr is the restricted semigroup of associated to the inverse semigroup S. We use this to give a characterization of module amenability of restricted semigroup algebra l1r (S) with the canonical action, where S is a Clifford semigroup.

Weak module amenability of triangular Banach algebras

2011 ◽  
Vol 61 (6) ◽  
Author(s):  
Abdolrasoul Pourabbas ◽  
Ebrahim Nasrabadi
Keyword(s):  
Banach Algebra ◽  
Banach Algebras ◽  
Module Amenability ◽  
Weak Amenability ◽  
Weak Module ◽  
Triangular Banach Algebras

AbstractLet A and B be unital Banach algebras and let M be a unital Banach A,B-module. Forrest and Marcoux [6] have studied the weak amenability of triangular Banach algebra $\mathcal{T} = \left[ {_B^{AM} } \right]$ and showed that T is weakly amenable if and only if the corner algebras A and B are weakly amenable. When $\mathfrak{A}$ is a Banach algebra and A and B are Banach $\mathfrak{A}$-module with compatible actions, and M is a commutative left Banach $\mathfrak{A}$-A-module and right Banach $\mathfrak{A}$-B-module, we show that A and B are weakly $\mathfrak{A}$-module amenable if and only if triangular Banach algebra T is weakly $\mathfrak{T}$-module amenable, where $\mathfrak{T}: = \{ [^\alpha _\alpha ]:\alpha \in \mathfrak{A}\} $.

Super module amenability of inverse semigroup algebras

2012 ◽  
Vol 86 (2) ◽  
pp. 279-288 ◽  
Author(s):  
M. Lashkarizadeh Bami ◽  
M. Valaei ◽  
M. Amini
Keyword(s):  
Inverse Semigroup ◽  
Semigroup Algebras ◽  
Module Amenability

Weak module amenability of triangular banach algebras II

2019 ◽  
Vol 69 (2) ◽  
pp. 425-432
Author(s):  
Ebrahim Nasrabadi
Keyword(s):  
Banach Algebra ◽  
Banach Algebras ◽  
Special Structure ◽  
Module Amenability ◽  
Weak Module ◽  
Triangular Banach Algebras

Abstract Let A and B be Banach 𝔄-bimodule and Banach 𝔅-bimodule algebras, respectively. Also let M be a Banach A, B-module and Banach 𝔄, 𝔅-module with compatible actions. In the case of 𝔄 = 𝔅, the author along with Pourabbas [5] have studied the weak 𝔄-module amenability of triangular Banach algebra $\begin{array}{} \displaystyle \mathcal{T}=\left[\begin{array}{rr} A & M \\ & B \end{array} \right] \end{array}$ and showed that 𝓣 is weakly 𝔄-module amenable if and only if the corner Banach algebras A and B are weakly 𝔄-module amenable, where A, B and M are unital. In this paper we investigate a special structure of 𝔄 ⊕ 𝔅-bimodule derivation from 𝓣 into 𝓣∗ and show that 𝓣 is weakly 𝔄 ⊕ 𝔅-bimodule amenable if and only if the corner Banach algebras A and B are weakly 𝔄-module amenable and weakly 𝔅-module amenable, respectively, where A, B and M are essential and not necessary unital.

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