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Some notions of amenability for certain products of Banach algebras

Eghbal Ghaderi; Rasoul Nasr-Isfahani; Mehdi Nemati — 2013

Colloquium Mathematicae

For two Banach algebras and ℬ, an interesting product $\times_{θ} ℬ$ , 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.

Approximate biflatness and Johnson pseudo-contractibility of some Banach algebras

Amir Sahami; Mohammad R. Omidi; Eghbal Ghaderi; Hamzeh Zangeneh — 2020

Commentationes Mathematicae Universitatis Carolinae

We study the structure of Lipschitz algebras under the notions of approximate biflatness and Johnson pseudo-contractibility. We show that for a compact metric space $X$ , the Lipschitz algebras ${Lip}_{α} (X)$ and ${lip}_{α} (X)$ are approximately biflat if and only if $X$ is finite, provided that $0 < α < 1$ . We give a necessary and sufficient condition that a vector-valued Lipschitz algebras is Johnson pseudo-contractible. We also show that some triangular Banach algebras are not approximately biflat.

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