Explicit representations of L. Schwartz’ spaces and by the sequence spaces and , respectively, for

The isomorphism of L. Schwartz’ spaces D L p and D ′ L p with the sequence spaces s ⊗ ˆ l p and s ′ ⊗ ˆ l p , respectively, goes back to a conjecture by A. Grothendieck and was proven by M. Valdivia and D. Vogt in a non-constructive way. We give a new constructive proof of these isomorphisms in the case 1 < p < ∞ .