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Displaying similar documents to “A generalized notion of n -weak amenability”

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.

Problems concerning n -weak amenability of a Banach algebra

Alireza Medghalchi, Taher Yazdanpanah (2005)

Czechoslovak Mathematical Journal

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In this paper we extend the notion of n -weak amenability of a Banach algebra 𝒜 when n . Technical calculations show that when 𝒜 is Arens regular or an ideal in 𝒜 * * , then 𝒜 * is an 𝒜 ( 2 n ) -module and this idea leads to a number of interesting results on Banach algebras. We then extend the concept of n -weak amenability to n .

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.

Some notions of amenability for certain products of Banach algebras

Eghbal Ghaderi, Rasoul Nasr-Isfahani, Mehdi Nemati (2013)

Colloquium Mathematicae

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For two Banach algebras and ℬ, an interesting product × θ , called the θ-Lau product, was recently introduced and studied for some nonzero characters θ on ℬ. Here, we characterize some notions of amenability as approximate amenability, essential amenability, n-weak amenability and cyclic amenability between and ℬ and their θ-Lau product.