ISSN 2456-0235

International Journal of Modern Science and Technology

INDEXED IN 

​​​​​​​​​​​​​October 2018, Vol. 3, No. 10, pp. 203-207. 

​​​Certain Aspects of Normal Classes of Hilbert Space Operator

N. B. Okelo*
School 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 T be a Quasi - * - class A normal operator on a complex Hilbert space H. In this paper, we prove that if E is the Riesz idempotent for a non-zero isolated point λ of the spectrum of T ∈ B(H) of Quasi - * - class A normal operator, then E is self-adjoint and EH = ker(T − λ) = ker (T − λ)*. We will also prove a necessary and sufficient condition for T ⊗ S to be quasi - * - class A normal where T and S are both non-zero operators.

Keywords: Paranormal operators; Weyl’s theorem; * - class A normal operators; Quasi - * - class A normal operators.

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