ISSN 2456-0235

International Journal of Modern Science and Technology

INDEXED IN 

​​​​​​Vol. 2, No. 10, 2017, pp. 341-344. 

​

​On Numerical Range of Maximal Jordan Elementary Operator   

B. O. Okello, N. B. Okelo, O. Ongati
School of Mathematics and Actuarial Science, Jaramogi Oginga Odinga University of Science and Technology, P.O. Box 2010-40601, Bondo- Kenya.
​​​*Corresponding author’s e-mail: bnyaare@yahoo.com

​Abstract
Studies on numerical ranges such as essential numerical ranges, spatial numerical ranges, algebraic numerical ranges and maximal numerical ranges for elementary operators have been considered by different scholars. In this paper we focus on maximal numerical range for a Jordan elementary operator. The results in this paper show that if H is an infinite dimensional complex Hilbert space and B(H) the algebra of all bounded linear operators on H, then the maximal numerical range M(U) of a Jordan elementary operator is nonempty, closed and convex. Furthermore we show that the maximal numerical radius is equivalent to the norm of Jordan elementary operator but are not necessarily equal.

Keywords: Numerical range; Maximal numerical range; Numerical radius; Norm and Jordan elementary operator. 

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