Orthogonality of algebraic elementary operators when their numerical ranges are spheroidal

10.30495/maca.2025.2055200.1132
Volume 7, Issue 2
Spring 2025
Pages 31-46

Document Type : Original Article

Authors

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

Abstract
Characterizations involving algebraic elementary operators have been done over the years, for instance, orthogonality when the operators are induced by other different types of transformations. In particular, algebraic elementary operators induced by norm-attainable maps have not been characterized in terms of orthogonality when their numerical ranges have spheroid boundaries. In this note, we characterize algebraic elementary operators in terms of Birkhoff-James orthogonality when they are induced by norm-attainable maps and the boundaries of their numerical ranges are spheroidal in shape. We show that under the pheroidicity criterion for the numerical range boundary, various types of algebraic elementary operators satisfy Birkhoff-James orthogonality.

Keywords

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  • Receive Date 06 March 2025
  • Revise Date 24 March 2025
  • Accept Date 09 April 2025