Interpolation of Fremlin tensor products and Schur factorization of matrices

Within finite dimensional Banach lattices we prove interpolation formulas for the Fremlin tensor product and spaces of regular multilinear forms and operators. We show applications to factorization of matrices with respect to the Schur product. Our results imply various abstract variants of Schurʼs classical result, and in particular we extend Pisierʼs converse for matrices in finite dimensional ℓp-spaces to the setting of complex Calderón interpolation of finite dimensional Banach lattices.