Higher projective tensor products of $c_0$

Abstract

Let m, n be positive integers with m < n. Under certain assumptions on the Banach space X, we prove that the n-fold projective tensor product of X, ⊗ n π X, is not isomorphic to any subspace of any quotient of the m-fold projective tensor product, ⊗ m π X.In particular, we prove that ⊗ n π c 0 is not isomorphic to any subspace of any quotient of ⊗ m π c 0 . This answers a question from [7].