Positive bilinear operators in Calderon-Lozanovskii spaces

A generalization of an abstract Holder-Rogers inequality for positive bilinear operators is proved. Then it is used in the theory of interpolation of operators. An interpolation theorem for positive bilinear operators between Calderon-Lozanovskii spaces holds if and only if the parameter functions generating those spaces satisfy a generalized C-supermultiplicativity condition (2). In the case when all generating functions are the same this condition is exactly the same as the C-supermultiplicativity condition on the function.