Interpolation of abstract Cesaro, Copson and Tandori spaces

TL;DR

This paper investigates the interpolation properties of abstract Cesàro, Copson, and Tandori spaces, providing new generalizations and revealing differences in behavior between finite and infinite intervals.

Contribution

It offers new descriptions of interpolation for these spaces, including Calderón-Lozanovski{1} construction, extending known results for Cesàro spaces.

Findings

Interpolation differs significantly between finite and infinite intervals.

New results for complex and real interpolation methods.

Generalizations to broader classes of interpolation functors.

Abstract

We study real and complex interpolation of abstract Ces\`aro, Copson and Tandori spaces, including the description of Calder\'on-Lozanovski{\v \i} construction for those spaces. The results may be regarded as generalizations of interpolation for Ces\`aro spaces $Ces_p(I)$ in the case of real method, but they are new even for $Ces_p(I)$ 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 Ces\`aro function spaces in the cases of finite and infinite interval.