scholarly journals Amenability of A⊕_T X as an extension of Banach algebra

2020 ◽  
Vol 49 ◽  
pp. 39-48
Author(s):  
M. Ghorbai ◽  
◽  
Davood Ebrahimi Bagha
Keyword(s):  
Banach Algebra ◽  
Banach Algebras ◽  
Linear Mapping ◽  
Module Amenability ◽  
Weak Module ◽  
Approximate Amenability

Let 𝐴𝐴,𝑋𝑋,𝔘𝔘 be Banach algebras and 𝐴𝐴 be a Banach 𝔘𝔘-bimodule also 𝑋𝑋 be a Banach 𝐴𝐴−𝔘𝔘-module. In this paper we study the relation between module amenability, weak module amenability and module approximate amenability of Banach algebra 𝐴𝐴⊕𝑇𝑇𝑋𝑋 and that of Banach algebras 𝐴𝐴,𝑋𝑋. Where 𝑇𝑇: 𝐴𝐴×𝐴𝐴→𝑋𝑋 is a bounded bi-linear mapping with specificconditions.

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.

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}\} $.

scholarly journals Module amenability, module character biprojectivity and module character biflatness of lau product of two Banach algebras

Filomat ◽  
2018 ◽  
Vol 32 (19) ◽  
pp. 6627-6641
Author(s):  
H. Sadeghi ◽  
Bami Lashkarizadeh
Keyword(s):  
Banach Algebra ◽  
Banach Algebras ◽  
Module Amenability ◽  
Character Amenability ◽  
Module Homomorphism ◽  
Approximate Amenability

Let A be a Banach algebra and T be an U-module homomorphism from U-bimodule B into U-bimodule A. We investigate module amenability (resp. module approximate amenability), module character amenability (resp. module character approximate amenability), module character biprojectivity and module character biflatness of A x Tu B for every two Banach U-bimodule A and B.

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.

scholarly journals n-Weak Module Amenability of Triangular Banach Algebras

2015 ◽  
Vol 65 (3) ◽  
Author(s):  
Abasalt Bodaghi ◽  
Ali Jabbari
Keyword(s):  
Banach Algebra ◽  
Banach Algebras ◽  
Current Paper ◽  
Module Amenability ◽  
Weak Module ◽  
Arens Regularity ◽  
Triangular Banach Algebras

AbstractLet 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 -

scholarly journals Weak module amenability for the second dual of a Banach algebra

2021 ◽  
Vol 25 (2) ◽  
pp. 297-306
Author(s):  
Shabani Soltanmoradi ◽  
Davood Ebrahimi Bagha ◽  
Pourbahri Rahpeyma
Keyword(s):  
Banach Algebra ◽  
Banach Algebras ◽  
Module Amenability ◽  
Banach Modules ◽  
Weak Module ◽  
Module Derivation ◽  
Second Dual

In this paper we study the weak module amenability of Banach algebras which are Banach modules over another Banach algebra with compatible actions. We show that for every module derivation D : A ↦ ( A/J_A )∗ if D∗∗(A∗∗) ⊆ WAP (A/J_A ), then weak module amenability of A∗∗ implies that of A. Also we prove that under certain conditions for the module derivation D, if A∗∗ is weak module amenable then A is also weak module amenable.

scholarly journals -Approximately Contractible Banach Algebras

2012 ◽  
Vol 2012 ◽  
pp. 1-20 ◽  
Author(s):  
M. Momeni ◽  
T. Yazdanpanah ◽  
M. R. Mardanbeigi
Keyword(s):  
Banach Algebra ◽  
Banach Algebras ◽  
Dense Range ◽  
Approximate Amenability

We investigate -approximate contractibility and -approximate amenability of Banach algebras, which are extensions of usual notions of contractibility and amenability, respectively, where is a dense range or an idempotent bounded endomorphism of the corresponding Banach algebra.

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 The Structure ofφ-Module Amenable Banach Algebras

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Mahmood Lashkarizadeh Bami ◽  
Mohammad Valaei ◽  
Massoud Amini
Keyword(s):  
Inverse Semigroup ◽  
Banach Algebra ◽  
Banach Algebras ◽  
Module Amenability ◽  
Banach Modules ◽  
Finite Set

We study the concept ofφ-module amenability of Banach algebras, which are Banach modules over another Banach algebra with compatible actions. Also, we compare the notions ofφ-amenability andφ-module amenability of Banach algebras. As a consequence, we show that, ifSis an inverse semigroup with finite setEof idempotents andl1Sis a commutative Banachl1E-module, thenl1S**isφ**-module amenable if and only ifSis finite, whenφ∈Homl1El1Sis an epimorphism. Indeed, we have generalized a well-known result due to Ghahramani et al. (1996).

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.

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