Higher order derivatives of analytic families of Banach spaces

F\'elix Cabello S\'anchez; Jes\'us M. F. Castillo; Willian H. G. Correa

Higher order derivatives of analytic families of Banach spaces

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arxiv 1906.06677 v2 pith:CCCOUDV3 submitted 2019-06-16 math.FA

Félix Cabello Sánchez , Jesús M. F. Castillo , Willian H. G. Correa This is my paper · ORCID

classification math.FA

keywords spacesfamiliesanalyticbanachcomplexinducedinterpolationrochberg

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We show that the Rochberg spaces induced by complex interpolation form themselves complex interpolation scales, obtain the interpolated spaces and associated derivations. We present our results in the context of analytic families of Banach spaces and study the problem of determining the Rochberg spaces induced by these new families.

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A single abstract theorem about pairs of interpolators unifies the commutator theorems of Cwikel-Kalton-Milman-Rochberg, Carro-Cerda-Soria, and translation operators, together with new symmetry, stability, and incompa...

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