The Butterfly lemma. (February 2022)

• Record Type: Journal Article
• Authors: Castillo, Jesús M.F.; Morales, Daniel
• Is Part Of: Nonlinear analysis. Volume 215(2022)
• Publication Date: 2022-02
• Subjects: Complex interpolation -- Factorization -- Quasilinear maps -- Differentials of complex interpolation processes; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2021.112630
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: The Butterfly lemma we present can be considered a reiteration theorem for differentials generated from a complex interpolation process for families of Köthe 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.