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1-amenability of 𝒜(X) for Banach spaces with 1-unconditional bases

A. Blanco (2012)

Studia Mathematica

The main result of the note is a characterization of 1-amenability of Banach algebras of approximable operators for a class of Banach spaces with 1-unconditional bases in terms of a new basis property. It is also shown that amenability and symmetric amenability are equivalent concepts for Banach algebras of approximable operators, and that a type of Banach space that was long suspected to lack property 𝔸 has in fact the property. Some further ideas on the problem of whether or not amenability (in...

2-normed Algebras-I

Neeraj Srivastava, S. Bhattacharya, S. N. Lal (2010)

Publications de l'Institut Mathématique

2-normed Algebras-II

Neeraj Srivastava, S. Bhattacharya, S. N. Lal (2011)

Publications de l'Institut Mathématique

3-Weak amenability of (2n)th duals of Banach algebras

Mina Ettefagh (2012)

Colloquium Mathematicae

We show that under some conditions, 3-weak amenability of the (2n)th dual of a Banach algebra A for some n ≥ 1 implies 3-weak amenability of A.

(Non-)amenability of ℬ(E)

Volker Runde (2010)

Banach Center Publications

In 1972, the late B. E. Johnson introduced the notion of an amenable Banach algebra and asked whether the Banach algebra ℬ(E) of all bounded linear operators on a Banach space E could ever be amenable if dim E = ∞. Somewhat surprisingly, this question was answered positively only very recently as a by-product of the Argyros-Haydon result that solves the “scalar plus compact problem”: there is an infinite-dimensional Banach space E, the dual of which is ℓ¹, such that $ℬ (E) = (E) + ℂ i d_{E}$ . Still, ℬ(ℓ²) is not amenable,...

$Δ$ -weak character amenability of certain Banach algebras

Hamid Sadeghi (2019)

Archivum Mathematicum

In this paper we investigate $Δ$ -weak character amenability of certain Banach algebras such as projective tensor product $A \hat{\otimes} B$ and Lau product $A \times_{θ} B$ , where $A$ and $B$ are two arbitrary Banach algebras and $θ \in Δ (B)$ , the character space of $B$ . We also investigate $Δ$ -weak character amenability of abstract Segal algebras and module extension Banach algebras.

$ϕ$ -multipliers on a class of topological algebras

Ali Naziri-Kordkandi (2022)

Mathematica Bohemica

In this paper, we generalize the concept of $ϕ$ -multipliers on Banach algebras to a class of topological algebras. Then the characterizations of $ϕ$ -multipliers are investigated in these algebras.