International Journal of Modern Science and Technology · ISSN 2456-0235

Research Article · Mathematical Sciences · Volume 2, Issue 3 · Mar 2017 · Pages 85–89

Characterization of Numerical Ranges of Posinormal Operator

S. Asamba, R. K. Obogi, N. B. Okelo

  • S. Asamba: Department of Mathematics, Kisii University, P.O. Box 408-40200, Kisii. Kenya.
  • R. K. Obogi: Department of Mathematics, Kisii University, P.O. Box 408-40200, Kisii. Kenya.
  • N. B. Okelo: School of Mathematics and Actuarial Science, Jaramogi Oginga Odinga University of Science and Technology, P.O. Box 210-40601, Bondo-Kenya.

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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