Vector Measures with Values in l^(∞)(Γ) and Interpolation of Banach Lattices

An explicit construction for the representation of the Calderón interpolation of spaces of vector measure integrable functions is given as well as for the representation of the real interpolation of these spaces using the K-functional. In order to do this, we introduce a technique based on interpolation of function valued matrices. For the real interpolation, we develop a vector-valued version of the K-functional having values in l∞-spaces, providing in this way a new procedure for the study of the interpolation of general Banach lattices.