On Interpolation of Vector – Valued Banach Lattices and Calderón – Lozanovskii Construction

We establish the connection between the variants of Schechter's complex interpolation methods, Peetre – Gustavsson's interpolation methods, and the Calderón – Lozanovskii construction on vector – valued Banach lattices. As applications, we show that the uniform convexity and the UMD property are stable by interpolation.