For 1/p+ 1/q<_l, we study the closed ideal ~3r formed by the (co, p, q)-summing operators. It turns out that T : X--+Y does not belong to 913~o,p,q if and only if it factors the map Id : lp. --+lq. By localization, we get the ideal es that consists of those operators T for *-Co ,p,q ~uper which all ultrapowers T u are contained in ~3Co,p,q. Operators in the complement of ~o,p,q are characterized by the property that they factor the maps Id : l~, -+ l~ uniformly. Our main tools are ideal norms.
NotationThroughout, we adopt the standard notation used in [P-W]. In particular, t2(X, Y) stands for the set of all (bounded linear) operators acting from a Banach space X into a Banach space Y, and we let lip + 1/p* = 1.