The Butterfly lemma

TL;DR

The paper introduces the Butterfly lemma, a reiteration theorem for differentials from complex interpolation of K"othe spaces, clarifying how configurations affect differentials and refining aspects of Kalton's interpolation theorem.

Contribution

It presents the Butterfly lemma, enhancing understanding of differential behavior in complex interpolation and refining existing theorems in the field.

Findings

Clarifies the effect of configurations on differentials.

Refines aspects of Kalton's interpolation theorem.

Provides a new reiteration theorem for K"othe spaces.

Abstract

The Butterfly lemma we present can be considered a reiteration theorem for differentials generated from a complex interpolation process for families of K\"othe spaces. The lemma will be used to clarify the effect of different configurations in the resulting differential (because although interpolation is an orientation-free process, the obtention of differentials is not) and to round off a few aspects of Kalton's interpolation theorem.