The Intersection of Similarity and Metric Equivalence Relations of Operators

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Published: 2023-01-21

Page: 14-23


Nzimbi Bernard Mutuku *

Department of Mathematics, Faculty of Science and Technology, University of Nairobi, Kenya.

Moindi Stephen Kibet

Department of Mathematics, Faculty of Science and Technology, University of Nairobi, Kenya.

Luketero Stephen Wanyonyi

Department of Mathematics, Faculty of Science and Technology, University of Nairobi, Kenya.

*Author to whom correspondence should be addressed.


Abstract

In this paper, we define the intersection of similarity and metric equivalence relations. We investigate the resulting equivalence relation of operators(metro-similarity) acting on finite dimensional separable complex Hilbert spaces. We then give conditions under which two operators are metro-similar.

Keywords: metric equivalence, similar, equivalence relation, finite rank


How to Cite

Mutuku, N. B., Kibet, M. S., & Wanyonyi, L. S. (2023). The Intersection of Similarity and Metric Equivalence Relations of Operators. Asian Journal of Pure and Applied Mathematics, 5(1), 14–23. Retrieved from https://globalpresshub.com/index.php/AJPAM/article/view/1726

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