Interpolation of abstract Cesà ro, Copson and Tandori spaces

We study real and complex interpolation of abstract Cesàro, Copson and Tandori spaces, including the description of Calderón-Lozanovskiǐ construction for those spaces. The results may be regarded as generalizations of interpolation for Cesàro spaces Cesp(I) in the case of real method, but they are new even for Cesp(I) in the case of complex method. Some results for more general interpolation functors are also presented. The investigations show an interesting phenomenon that there is a big difference between interpolation of Cesàro function spaces in the cases of finite and infinite interval.