A note on p-limited sets in dual Banach spaces

If A is a bounded subset of X^* and ℓ _∞ (A) is the Banach space (sup norm) of all bounded real-valued functions defined on A, let E: X→ℓ _∞ (A) be the evaluation map defined by Ex(x^*)= x^*(x) , x∈ X , x^*∈ A . We show that a subset A of X^* is a p-limited set if and only if E: X→ℓ _∞ (A) is p-summing. We give a characterization of p-limited sets in X^* using w^* -w operators T:X^*→ℓ _p .