Closed ideals with bounded $\Delta$-weak approximate identities in some   certain Banach algebras
  It is shown that a locally compact group $G$ is amenable if and only if some certain closed ideals of the Fig\`{a}-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 $C_{0}^{w}(G)$. 
Javad Laali and Mohammad Fozouni
math.FA