Derivation of vector-valued complex interpolation scales

TL;DR

This paper investigates vector-valued complex interpolation scales, analyzing their properties and providing examples that challenge existing assumptions about their triviality and singularity.

Contribution

It introduces new examples and insights into the properties of vector-valued complex interpolation scales, expanding understanding beyond previous theorems.

Findings

Identifies conditions under which interpolation scales are trivial or singular.

Provides counterexamples to previous hypotheses in the literature.

Enhances understanding of the structure of complex interpolation scales.

Abstract

We study complex interpolation scales obtained by vector valued amalgamation and the derivations they generate. We study their trivial and singular character and obtain examples showing that the hypotheses in the main theorems of [J.M.F. Castillo, V. Ferenczi and M. Gonz\'alez, \emph{Singular exact sequences generated by complex interpolation}, Trans. Amer. Math. Soc. 369 (2017) 4671--4708] are not necessary.