On Spectral Properties of Orthogonal Isometries

Authors

  • Jacob Gachago Department of Pure and Applied Mathematics, Jaramogi Oginga Odinga University of Science and Technology, Box 210-40601, Bondo-Kenya.
  • Benard Okelo Department of Pure and Applied Mathematics, Jaramogi Oginga Odinga University of Science and Technology, Box 210-40601, Bondo-Kenya.
  • Willy Kangogo Department of Pure and Applied Mathematics, Jaramogi Oginga Odinga University of Science and Technology, Box 210-40601, Bondo-Kenya.

Keywords:

Spectrum, Operator, Isometry, Orthogonality

Abstract

Isometries are special mappings with a property of distance preservation. This property makes them unique and interesting in-terms of characterization. However, it is very difficult to do characterizations of properties of isometires in a general Banach space setting due to the intricate underlying structures in Banach spaces. In this paper, we characterize spectral properties of isometries and in particular when they are orthogonal. We show that orthogonal isometries preserve distance even when they are subjected to direct sum decomposition.

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Published

2025-08-13

How to Cite

Gachago, J., Okelo, B., & Kangogo, W. (2025). On Spectral Properties of Orthogonal Isometries. International Journal of Open Problems in Computer Science and Mathematics, 18(4), 12–30. Retrieved from https://ijopcm.icsrs.uk/index.php/journal/article/view/37

Issue

Vol. 18 No. 4 (2025): Int. J. Open Problems Compt. Math., Vol. 18, No. 4, December 2025

Section

Articles