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Essential S-Spectrum for Quaternionic Quasi-Compact Operators on Right Quaternionic Hilbert Spaces

Essential S-Spectrum for Quaternionic Quasi-Compact Operators on Right Quaternionic Hilbert Spaces The aim of this concept is to study the existence of eigenvalues far from the essential S-spectra on quaternionic Hilbert spaces and also to search the instability of the essential S-spectra under every perturbation. Besides, this paper is devoted to the investigation of the stability of the Weyl essential S-spectrum of linear operator A\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$A$\end{document} subjected to additive perturbation K\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$K$\end{document} such that (AK+KA+K2−2Re(q)K)Rq(A+K)−1\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$(AK+KA+K^{2}-2\operatorname{Re}(\mathbf{q})K)R_{\mathbf{q}}(A+K)^{-1}$\end{document} or Rq(A+K)−1(AK+KA+K2−2Re(q)K)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$R_{\mathbf{q}}(A+K)^{-1} (AK+KA+K^{2}-2\operatorname{Re}(\mathbf{q})K)$\end{document} is a quasi-compact operator. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Applicandae Mathematicae Springer Journals

Essential S-Spectrum for Quaternionic Quasi-Compact Operators on Right Quaternionic Hilbert Spaces

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Publisher
Springer Journals
Copyright
Copyright © The Author(s), under exclusive licence to Springer Nature B.V. 2021
ISSN
0167-8019
eISSN
1572-9036
DOI
10.1007/s10440-021-00441-2
Publisher site
See Article on Publisher Site

Abstract

The aim of this concept is to study the existence of eigenvalues far from the essential S-spectra on quaternionic Hilbert spaces and also to search the instability of the essential S-spectra under every perturbation. Besides, this paper is devoted to the investigation of the stability of the Weyl essential S-spectrum of linear operator A\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$A$\end{document} subjected to additive perturbation K\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$K$\end{document} such that (AK+KA+K2−2Re(q)K)Rq(A+K)−1\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$(AK+KA+K^{2}-2\operatorname{Re}(\mathbf{q})K)R_{\mathbf{q}}(A+K)^{-1}$\end{document} or Rq(A+K)−1(AK+KA+K2−2Re(q)K)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$R_{\mathbf{q}}(A+K)^{-1} (AK+KA+K^{2}-2\operatorname{Re}(\mathbf{q})K)$\end{document} is a quasi-compact operator.

Journal

Acta Applicandae MathematicaeSpringer Journals

Published: Dec 1, 2021

Keywords: Quaternions; Quasi-compact; Quaternionic Hilbert spaces; Essential S-spectra; 47A06

References