The Intersection of Similarity and Metric Equivalence Relations of Operators
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