A study is made of the norm wp (1 ≤ p ≤ ∞) on the tensor product of two Banach spaces E and F. It is shown that wp is a tensor norm, and a representation is deduced for the elements in the completion\(E\tilde \otimes _{w_p } F\) of E ⊗ F equipped with wp. Finally it is shown that the wp-nuclear operators in the sense of Grothendieck [3] coincide with those operators factoring compactly throughp (if 1 ≤ p ≤ ∞) or Co (if p=∞), with related equalities concerning the idea1 norms.