X iv :m at h/ 05 02 30 2v 1 [ m at h. FA ] 1 5 Fe b 20 05 OH-TYPE AND OH-COTYPE OF OPERATOR SPACES AND COMPLETELY SUMMING MAPS HUN HEE LEE Abstract. The definition and basic properties of OH-type and OH-cotype of operator spaces are given. We prove that every bounded linear map from C(K) into OH-cotype q (2 ≤ q < ∞) space (including most of commutative Lq-spaces) for a compact set K satisfies c...

Given p ≥ 1, we denote by Cp the class of all Banach spaces X satisfying the equality Kp(Y,X) = Πp(Y,X) for every Banach space Y , Kp (respectively, Πp) 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-...