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

Abstract

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