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Differential processes generated by two interpolators
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas ( IF 2.9 ) Pub Date : 2020-08-12 , DOI: 10.1007/s13398-020-00920-5
Jesús M. F. Castillo , Willian H. G. Corrêa , Valentin Ferenczi , Manuel González

We study couples of interpolators, the differentials they generate and their associated commutator theorems. An essential part of our analysis is the study of the intrinsic symmetries of the process. Since we work without any compatibility or categorical assumption, our results are flexible enough to generalize most known results for commutators or translation operators, in particular those of Cwikel, Kalton, Milman, Rochberg \cite{ckmr} for differential methods and those of Carro, Cerda and Soria \cite{caceso} for compatible interpolators. We also generalize stability and singularity results in \cite{cfg,ccfg,correa} from the complex method to general differential methods and obtain new incomparability results.

中文翻译:

两个内插器产生的微分过程

我们研究了一对内插器、它们产生的微分及其相关的换向器定理。我们分析的一个重要部分是研究过程的内在对称性。由于我们在没有任何兼容性或分类假设的情况下工作,因此我们的结果足够灵活,可以概括大多数已知的交换子或翻译算子的结果,特别是 Cwikel、Kalton、Milman、Rochberg \cite{ckmr} 的差分方法和 Carro 的结果Cerda 和 Soria \cite{caceso} 用于兼容的插值器。我们还将 \cite{cfg,ccfg,correa} 中的稳定性和奇异性结果从复数方法推广到一般微分方法,并获得新的不可比性结果。
更新日期:2020-08-12
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