A note on complex interpolation and Calder\'on product of quasi-Banach spaces

TL;DR

This paper extends classical interpolation results by proving that the inner complex interpolation of quasi-Banach lattices equals the closure of their intersection in the Calderón product, generalizing Shestakov's 1974 Banach lattice result.

Contribution

It generalizes a classical interpolation theorem from Banach lattices to quasi-Banach lattices, establishing the equivalence of inner complex interpolation and the closure of intersection in Calderón products.

Findings

Inner complex interpolation coincides with the closure of intersection in Calderón product for quasi-Banach lattices.

Generalizes Shestakov's classical result from Banach to quasi-Banach lattices.

Provides a new understanding of interpolation in the quasi-Banach setting.

Abstract

In this paper, we prove that the inner complex interpolation of two quasi-Banach lattices coincides with the closure of their intersection in their Calder\'on product. This generalizes a classical result by Shestakov in 1974 for Banach lattices.