On the interpolation of injective or projective tensor products of Banach spaces

AbstractWe prove a general result on the factorization of matrix-valued analytic functions. We deduce from it that if (E0, E1) and (F0, F1) are interpolation pairs with dense intersections, then under some conditions on the spaces Ei, Fi, we have [E0\̂bo F0, E1\̂bo F1]θ = [E0, E1]θ\̂bo [F0, F1]θ, 0 < θ < 1. We find also conditions on the spaces Ei, Fi, so that the following holds: [E0\̆bo F0, E1\̆bo F1]θ = [E0, E1]θ\̆bo [F0, F1]θ, 0 < θ < 1. Some applications of these results are also Considered