CONICET | Buscador de Institutos y Recursos Humanos

We study the space of p-compact operators, Kp, using the theory of tensor norms and operator ideals. We prove that Kp is associated to =dp, the left injective associate of the Chevet-Saphar tensor norm dp. This allows us to relate the theory of p-summing operators to that of p-compact operators. Using the results known for the former class and appropriate hypotheses on E and F we prove that Kp(E; F) is equal to Kq(E; F) for a wide range of values of p and q, and show that our results are sharp. We also exhibit several structural properties of Kp. For instance, we show that Kp is regular, surjective, and totally accessible, and we characterize its maximal hull Kp^max as the dual ideal of p-summing operators. Furthermore, we prove that Kp coincides isometrically with the dual to the ideal of the quasi p-nuclear operators.