Kato S-Spectrum in the Quaternionic Setting

被引：0

作者：

K. Thirulogasanthar

B. Muraleetharan

机构：

[1] Concordia University,Department of Computer Science and Software Engineering

[2] University of Jaffna,Department of Mathematics and Statistics

来源：

Advances in Applied Clifford Algebras | 2020年 / 30卷

关键词：

Quaternions; Quaternionic Hilbert spaces; S-spectrum; Semi-regular operator; Approximate S-point spectrum; Surjectivity ; -spectrum; Kato S-spectrum; Primary 47A10; 47A11; 47A25;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

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.

引用

共 30 条

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