International Journal of Modern Science and Technology

INDEXED IN 

ISSN 2456-0235

ISSN 2456-0235

​​​​​International Journal of Modern Science and Technology, Vol. 2, No. 3, 2017, Pages 85-89. 

​

​Characterization of Numerical Ranges of Posinormal Operator

S. Asamba¹, R. K. Obogi¹, N. B. Okelo²,*
​¹Department of Mathematics, Kisii University, P.O. Box 408-40200, Kisii. Kenya.
²School of Mathematics and Actuarial Science, Jaramogi Oginga Odinga University of Science and Technology, P.O. Box 210-40601, Bondo-Kenya.
*Corresponding author’s e-mail: bnyaare@yahoo.com

​Abstract
Let be a complex Hilbert space equipped with the inner product ; and let  be the algebra of bounded linear operators acting on. The numerical range of a bounded linear operator  on a complex Hilbert space is the set  The numerical radius of  is given by . In this paper we investigate the numerical range of an operator acting on a complex Hilbert space. In particular, we characterize the numerical range of a posinormal operator on an infinite dimensional complex Hilbert space. The present paper shows that for a posinormal operator A, W(A) is nonempty, always and  is an ellipse whose foci are the eigenvalues of A.

​​Keywords: Numerical range; Linear operator; Posinormal operator; Hilbert Space.

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