In this paper we introduce an axiomatic approach to the theory of s-numbers in quaternionic analysis. To this end, Pietsch’s approach to s-number theory is adapted to the quaternionic framework, following the works of Colombo and Sabadini on quaternionic spectral analysis. One of the main results of this paper is the uniqueness of s-numbers over quaternionic Hilbert spaces. Moreover, examples are given in the quaternionic framework together with the introduction of nuclear numbers. A consequence of the presented theory is a basis independent definition of the Schatten classes over quaternionic Hilbert and Banach spaces.

中文翻译：

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四元分析和 Schatten 类中 s 数的概念

在本文中，我们介绍了四元数分析中 s 数理论的公理化方法。为此，Pietsch 的 s 数理论方法适应了四元数框架，遵循 Colombo 和 Sabadini 关于四元数谱分析的工作。本文的主要成果之一是四元数希尔伯特空间上 s 数的唯一性。此外，还给出了四元框架中的例子以及核数的介绍。所提出的理论的结果是四元数希尔伯特和巴纳赫空间上的 Schatten 类的基础独立定义。