Mathematical Analysis and its Contemporary Applications

Orthogonal projections approach to characterization of numerical ranges of elementary operators

10.30495/maca.2025.2053352.1128
Volume 7, Issue 1
Winter 2025
Pages 49-60
Mathematical Analysis and its Contemporary Applications

Document Type : Original Article

Authors

Otae Kelvin Odindo
Benard Okelo
Priscah Omoke

Department of Pure and Applied Mathematics, Jaramogi Oginga Odinga University of Science and Technology, Box 210-40601, Bondo, Kenya

Abstract
 Properties of elementary operators have been characterized over the years for instance numerical ranges the operators are implemented by other different types of operators. However, elementary operators implemented by orthogonal projections have not been characterized in terms of numerical ranges. In this paper,  we characterize elementary operators in terms of numerical ranges, when they are implemented by orthogonal projections.  The results show that the numerical range of a basic elementary operator satisfies the ellipsoidicity criterion. Moreover,  the numerical range of a Jordan elementary operator satisfies the spheroidicity criterion.

Keywords

Numerical range
Elementary operator
Orthogonal projection
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  • Receive Date 13 January 2025
  • Revise Date 16 February 2025
  • Accept Date 17 February 2025

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