In a number of places in the collective works of Nigel Kalton, there is an unproven claim that l_p(X) is a tensor-product. I think I can show it is isomorphic to the projective tensor-product of l_p and X but the proof is not "immediate" to me. Does anyone know if such a proof is simple? Anyone have a reference for this? Here 1
If p is in (0,1] and X is a p-Banach space then l_p(X) is isometric to a p-projective tensor-product of l_p and X. Here the 1-projective norm is the projective norm and if p
The case p>1 is also straight forward. So, the interesting question: If a tensor-product of l_1 and X has Rademacher type 1, must X be locally-convex?
Dear Geoff Diestel, you can benefit from this references :
1- Qingying Bu & Joe Diestel. OBSERVATIONS ABOUT THE PROJECTIVE TENSOR PRODUCT OF BANACH SPACES, I
2- Jan H. Fourie ∗,1 and Ilse M. Röntgen 2. Banach space sequences and projective tensor products
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