Characterization of the minimal and maximal operator ideals associated to the tensor norm defined by a sequence space

We characterize the minimal and maximal operator ideals associated, in the sense of Defant and Floret, to a wide class of tensor norms derived from a Banach sequence space. Our results are extensions of classical ones about tensor norms of Saphar [Studia Math. 38 (1972)71-100] and show the key role played by the structure of finite-dimensional subspaces in this kind of problems. (C) 2004 Elsevier Inc. All rights reserved.