In a right quaternionic Hilbert space, for a bounded right linear operator, the Kato S-spectrum is introduced and studied to a certain extent. In particular, it is shown that the Kato S-spectrum is a non-empty compact subset of the S-spectrum and it contains the boundary of the S-spectrum. Using right-slice regular functions, local S-spectrum, at a point of a right quaternionic Hilbert space, and the local spectral subsets are introduced and studied. The S-surjectivity spectrum and its connections to the Kato S-spectrum, approximate S-point spectrum and local S-spectrum are investigated. The generalized Kato S-spectrum is introduced and it is shown that the generalized Kato S-spectrum is a compact subset of the S-spectrum.

中文翻译：

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四元离子环境中的加藤S光谱

在右四元数希尔伯特空间中，对于有界右线性算子，在一定程度上引入了加藤S谱并对其进行了研究。特别地，显示出加藤S谱是S谱的非空紧凑子集，并且它包含S谱的边界。利用右切片正则函数，在右四元离子希尔伯特空间的一个点上引入局部S谱，并研究局部光谱子集。研究了S射影谱及其与Kato S谱，近似S点谱和局部S谱的联系。介绍了广义的Kato S谱，证明了广义的Kato S谱是S谱的紧凑子集。