On injective tensor powers of ℓ1

Abstract

In this paper we prove that the 3-fold injective tensor product ℓ1⊗ˆεℓ1⊗ˆεℓ1 is not isomorphic to any subspace of ℓ1⊗ˆεℓ1. This result provides a new solution to a problem of Diestel on the projective tensor products of c0. Moreover, this result implies that for any infinite countable compact metric space K, the 3-fold projective tensor product C(K)⊗ˆπC(K)⊗ˆπC(K) is not isomorphic to any quotient of C(K)⊗ˆπC(K).