Closed ideals with bounded $\Delta$-weak approximate identities in some certain Banach algebras

Abstract

It is shown that a locally compact group $G$ is amenable if and only if some certain closed ideals of the Figà-Talamanca-Herz algebra $A_p(G)$ admit bounded $\Delta$-weak approximate identities. Also, similar results are obtained for the function algebras $\mathfrak{L}A(G)$ and $C_0^w(G)$.

9 pages, To appear in Miskolc Math. Notes