Displaying similar documents to “Problems concerning $n$-weak amenability of a Banach algebra”

A generalized notion of n -weak amenability

Abasalt Bodaghi, Behrouz Shojaee (2014)

Mathematica Bohemica

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In the current work, a new notion of n -weak amenability of Banach algebras using homomorphisms, namely ( ϕ , ψ ) - n -weak amenability is introduced. Among many other things, some relations between ( ϕ , ψ ) - n -weak amenability of a Banach algebra 𝒜 and M m ( 𝒜 ) , the Banach algebra of m × m matrices with entries from 𝒜 , are studied. Also, the relation of this new concept of amenability of a Banach algebra and its unitization is investigated. As an example, it is shown that the group algebra L 1 ( G ) is ( ϕ , ψ )- n -weakly amenable...

Ideal amenability of module extensions of Banach algebras

Eshaghi M. Gordji, F. Habibian, B. Hayati (2007)

Archivum Mathematicum

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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.

Constructions preserving n -weak amenability of Banach algebras

A. Jabbari, Mohammad Sal Moslehian, H. R. E. Vishki (2009)

Mathematica Bohemica

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A surjective bounded homomorphism fails to preserve n -weak amenability, in general. We however show that it preserves the property if the involved homomorphism enjoys a right inverse. We examine this fact for certain homomorphisms on several Banach algebras.