Interpolation of abstract Cesaro, Copson and Tandori spaces

Abstract

We study real and complex interpolation of abstract Cesàro, Copson and Tandori spaces, including the description of Calderón-Lozanovski{\v ı} construction for those spaces. The results may be regarded as generalizations of interpolation for Cesàro spaces $Ce{s}_p(I)$ in the case of real method, but they are new even for $Ce{s}_p(I)$ 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.

22 pages