Amenable groups and bounded Δ-weak approximate identities

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Let A be a Banach algebra with a non-empty character space. We say that a bounded net {eα} in A is a bounded Δ-weak approximate identity for A if, for each a∈ A and compact subset K of Δ(A), ||eαa-a||ₖ=ϕ∈ ₖ|ϕ(eαa)-ϕ(a)|→ 0. For each 1<p<∞, we prove that the Figa-Talamanca Herz algebra, Aₚ(G) has a bounded Δ-weak approximate identity if and only if G is an amenable group. Also we give a sufficient condition for amenability of group G.