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Weak amenability of the second dual of a Banach algebra

M. Eshaghi GordjiM. Filali — 2007

Studia Mathematica

It is known that a Banach algebra inherits amenability from its second Banach dual **. No example is yet known whether this fails if one considers the weak amenability instead, but the property is known to hold for the group algebra L¹(G), the Fourier algebra A(G) when G is amenable, the Banach algebras which are left ideals in **, the dual Banach algebras, and the Banach algebras which are Arens regular and have every derivation from into * weakly compact. In this paper, we extend this class of...

Arens regularity of module actions

M. Eshaghi GordjiM. Filali — 2007

Studia Mathematica

We study the Arens regularity of module actions of Banach left or right modules over Banach algebras. We prove that if has a brai (blai), then the right (left) module action of on * is Arens regular if and only if is reflexive. We find that Arens regularity is implied by the factorization of * or ** when is a left or a right ideal in **. The Arens regularity and strong irregularity of are related to those of the module actions of on the nth dual ( n ) of . Banach algebras for which Z( **) = but Z t ( * * ) are...

Ideal amenability of module extensions of Banach algebras

Eshaghi M. GordjiF. HabibianB. Hayati — 2007

Archivum Mathematicum

Let 𝒜 be a Banach algebra. 𝒜 is called ideally amenable if for every closed ideal I of 𝒜 , the first cohomology group of 𝒜 with coefficients in I * is zero, i.e. H 1 ( 𝒜 , I * ) = { 0 } . Some examples show that ideal amenability is different from weak amenability and amenability. Also for n N , 𝒜 is called n -ideally amenable if for every closed ideal I of 𝒜 , H 1 ( 𝒜 , I ( n ) ) = { 0 } . In this paper we find the necessary and sufficient conditions for a module extension Banach algebra to be 2-ideally amenable.

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