No 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.

Abstract. In this paper we find necessary and sufficient conditions for weak amenability of the convolution Banach algebras A(K) and L 2 (K) for a compact hypergroup K, together with their applications to convolution Banach algebras L p (K) (2 ≤ p < ∞). It will further be shown that the convolution Banach algebra A(G) for a compact group G is weakly amenable if and only if G has a closed abelian subgroup of finite index.

In this paper the approximate weak amenability of abstract Segal algebras is investigated. Applications to compact groups are given. Also an open problem raised by Ghahramani and Lau is answered negatively.

In this paper, some relations between L p-spaces on locally compact groups are found. Applying these results proves that for a locally compact group G, the convolution Banach algebras L p(G) ∩ L 1(G) (1 < p ≤ ∞), and A p(G) ∩ L 1(G) (1 < p < ∞) are amenable if and only if G is discrete and amenable.