Interpolator symmetries and new Kalton-Peck spaces

TL;DR

This paper explores symmetries in interpolator diagrams within the Kalton-Montgomery complex interpolation framework, focusing on specific cases involving weighted 2 spaces and 1 spaces at 5=1/2, revealing new structural insights.

Contribution

It provides a detailed analysis of interpolator symmetries and introduces new Kalton-Peck spaces in the context of complex interpolation, especially for weighted 2 and 1 spaces.

Findings

Identification of symmetries in interpolator diagrams

New structural properties of Kalton-Peck spaces

Insights into interpolation at 5=1/2 for specific pairs

Abstract

Diagrams generated by three interpolators in an abstract Kalton-Montgomery complex like interpolation scheme. We will consider in detail the case of the first three Schechter interpolators associated to the usual Calder\'on complex interpolation method in two especially interesting cases: weighted $\ell_2$ spaces, i.e., interpolation pairs $(\ell_2(w^{-1}), \ell_2(w))_\theta$, and $\ell_p$ spaces, i.e., the interpolation pair $(\ell_\infty, \ell_1)_\theta$, both at $\theta=1/2$.