Given p ≥ 1, we denote by Cp the class of all Banach spaces X
satisfying the equality Kp(Y,X) = Πdp(Y,X) for every Banach space Y ,
Kp (respectively, Πdp
) being the operator ideal of p-compact operators
(respectively, of operators with p-summing adjoint). If X belongs
to Cp, a bounded set A ⊂ X is relatively p-compact if and only if
the evaluation map U∗
A : X∗ −→ ∞(A) is p-summing. We obtain
p-compactness criteria valid for Banach spaces in Cp
