Approximate semi-amenability of Banach algebras

Abstract

Let A be a Banach algebra, and X a Banach A-bimodule. A bounded linear mapping D : A → X is approximately semi-inner derivation if there eixist nets (ξ α ) α and (µ α ) α in X such that, for each a ∈ A, D(a) = lim α (a.ξ α − µ α .a). A is called approximately semi-amenable if for every Banach A-bimodule X , every D ∈ Z 1 (A, X * ) is approximtely semi-inner. There are some Banach algebras which are approximately semi-amenable, but not approximately amenable. In this manuscript, we investigate some properties of approximate semi-amenability of Banach algebras. Also in Theorem 2.7 we prove the approximate semi-amenability of Segal algebras on a locally compact group G.

Approximate semi-amenability of Banach algebras

“…The paper [22], by the same authors and one other, has the same oversight. More recently, the same authors have listed [23] on the arXiv. Unfortunately, there are numerous errors in [23].…”

“…More recently, the same authors have listed [23] on the arXiv. Unfortunately, there are numerous errors in [23].…”