Weak Amenability of Convolution Banach Algebras on Compact Hypergroups

Abstract

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.

Frechet algebras in abstract Harmonic analysis

“…In particular, B is weakly amenable if it is 1-weakly amenable. Recently, several papers dealing with this subject have appeared; see for example [28,53,60]. G 3.3.…”