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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...
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.
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 . Still, ℬ(ℓ²) is not amenable,...
In this paper we investigate -weak character amenability of certain Banach algebras such as projective tensor product and Lau product , where and are two arbitrary Banach algebras and , the character space of . We also investigate -weak character amenability of abstract Segal algebras and module extension Banach algebras.
In this paper, we generalize the concept of -multipliers on Banach algebras to a class of topological algebras. Then the characterizations of -multipliers are investigated in these algebras.
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