Calder\'on-Lozanovskii interpolation on quasi-Banach lattices

TL;DR

This paper extends the Calderón-Lozanovskii interpolation theory to quasi-Banach lattices, utilizing properties of regular operators to broaden understanding of associated interpolation methods.

Contribution

It provides an extension of Ovchinnikov's result on interpolation methods within the setting of quasi-Banach lattices, advancing the theoretical framework.

Findings

Extended Calderón-Lozanovskii construction to quasi-Banach lattices.

Connected interpolation methods $^c$ and $^0$ in this new context.

Utilized properties of $(,1)$-regular operators for the extension.

Abstract

We consider the Calder\'on-Lozanovskii construction $\varphi(X_0,X_1)$ in the context of quasi-Banach lattices and provide an extension of a result by V. I. Ovchinnikov concerning the associated interpolation methods $\varphi^c$ and $\varphi^0$. Our approach is based on the interpolation properties of $(\infty,1)$-regular operators between quasi-Banach lattices.