Essential Amenability of Abstract Segal Algebras

Abstract

A number of well-known results of Ghahramani and Loy on the essential amenability of Banach algebras are generalized. It is proved that a symmetric abstract Segal algebra with respect to an amenable Banach algebra is essentially amenable. Applications to locally compact groups are given.2000 Mathematics subject classification: primary 43A20.

Essential Amenability of Dual Banach Algebras

“…Setting D := D − ad x , we observe that D is an ω * -continuous derivation from A into X and D| B = 0. An argument similar to the proof of[11, Proposition 4.1] shows that D = 0 and so D = ad x , as required.…”

On Some Homological Properties of Hypergroup Algebras with Relation to Their Character Spaces

“…We note that there are some abstract Segal algebras which are not symmetric. Homological and cohomological properties of abstract Segal algebras have been studied in many papers (see, for example, [17][18][19]). Recall that it is known that Δ(B) � φ| B : φ ∈ Δ(A) 􏼈 􏼉 (see Lemma 2.2 in [1]).…”

$\Delta $-weak character amenability of certain Banach algebras

“…(3) there exists C > 0 such that ab B ≤ C a A b B for all a, b ∈ B. Several authors have studied various notions of amenability for abstract Segal algebras; see, for example, [14,2].…”