On The Interpolation of Injective or Projective Tensor Products of Banach Spaces
نویسنده
چکیده
We prove a general result on the factorization of matrix-valued analytic functions. We deduce that if (E0, E1) and (F0, F1) are interpolation pairs with dense intersections, then under some conditions on the spaces E0, E1, F0 and F1, we have [E0⊗̂F0, E1⊗̂F1]θ = [E0, E1]θ⊗̂[F0, F1]θ, 0 < θ < 1. We find also conditions on the spaces E0, E1, F0 and F1 , so that the following holds [E0 ∨ ⊗F0, E1 ∨ ⊗F1]θ = [E0, E1]θ ∨ ⊗[F0, F1]θ, 0 < θ < 1. Some applications of these results are also considered.
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