Explicit representations of L. Schwartz’ spaces DLpDLp and D′LpD′Lp by the sequence spaces s⊗ˆlp and s′⊗ˆlp, respectively, for 1<p<∞1<p<∞

The isomorphism of L. Schwartz’ spaces DLpDLp and D′LpD′Lp with the sequence spaces s⊗ˆlp and s′⊗ˆlp, 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