scholarly journals Morita Equivalence of Brandt Semigroup Algebras

2012 ◽  
Vol 2012 ◽  
pp. 1-7
Author(s):  
Maysam Maysami Sadr
Keyword(s):  
Banach Algebras ◽  
Morita Equivalence ◽  
Brandt Semigroup ◽  
Semigroup Algebras ◽  
Homology Groups ◽  
Fixed Group ◽  
Morita Theory ◽  
Morita Invariant ◽  
Brandt Semigroups ◽  
Approximate Amenability

We show that Banach semigroup algebras of any two Brandt semigroups over a fixed group are Morita equivalence with respect to the Morita theory of self-induced Banach algebras introduced by Grønbæk. As applications, we show that the bounded Hochschild (co)homology groups of Brandt semigroup algebras over amenable groups are trivial and prove that the notion of approximate amenability is not Morita invariant.

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.

scholarly journals WEAK FORMS OF AMENABILITY FOR BANACH ALGEBRAS

2011 ◽  
Vol 85 (3) ◽  
pp. 509-517
Author(s):  
H. SAMEA
Keyword(s):  
Banach Algebras ◽  
Compact Groups ◽  
Direct Sums ◽  
Approximate Amenability

AbstractIn this paper, the amenability and approximate amenability of weighted ℓp-direct sums of Banach algebras with unit, where 1≤p<∞, are completely characterized. Applications to compact groups and hypergroups are given.

A note on the approximate amenability of semigroup algebras

2009 ◽  
Vol 79 (2) ◽  
pp. 349-354 ◽  
Author(s):  
Filofteia Gheorghe ◽  
Yong Zhang
Keyword(s):  
Semigroup Algebras ◽  
Approximate Amenability

Module Approximate Amenability for Semigroup Algebras

2009 ◽  
Vol 9 (12) ◽  
pp. 2348-2350
Author(s):  
Taher Yazdanpana ◽  
Hashem Najafi
Keyword(s):  
Semigroup Algebras ◽  
Approximate Amenability

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.

Approximate amenability of Fréchet algebras

2008 ◽  
Vol 145 (2) ◽  
pp. 403-418 ◽  
Author(s):  
P. LAWSON ◽  
C. J. READ
Keyword(s):  
Banach Algebras ◽  
Approximate Identity ◽  
Approximate Identities ◽  
Continuous Point ◽  
Approximate Amenability

AbstractThe notion of approximate amenability was introduced by Ghahramani and Loy, in the hope that it would yield Banach algebras without bounded approximate identity which nonetheless had a form of amenability. So far, however, all known approximately amenable Banach algebras have bounded approximate identities (b.a.i.). In this paper we define approximate amenability and contractibility of Fréchet algebras, and we prove the analogue of the result for Banach algebras that these properties are equivalent. We give examples of Fréchet algebras which are approximately contractible, but which do not have a bounded approximate identity. For a good many Fréchet algebras without b.a.i., we find either that the algebra is approximately amenable, or it is “obviously” not approximately amenable because it has continuous point derivations. So the situation for Fréchet algebras is quite close to what was hoped for Banach algebras.

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