ISSN 2456-0235

International Journal of Modern Science and Technology


​​​​​​​​​February 2018, Vol. 3, No 2, pp 27-32. 

​​Necessary and Sufficient conditions for Normality of Operators in Hilbert spaces

A. M. Wafula, N. B. Okelo*, O. Ongati
School of Mathematics and Actuarial Science, Jaramogi Oginga Odinga University of Science and Technology, P.O. Box 2010-4060, Bondo-Kenya.
​​*Corresponding author’s e-mail:


Characterization of normality is an interesting aspect for Hilbert space operators. In this paper, we have shown that for an operator A to be normal, it is necessary that A = A*. It is also sufficient that for an operator A to be normal then the condition AA* = A*A holds. Moreover, for an inner derivation, we conjecture that the property ᵟA=ᵟA* is necessary for its normality.

Keywords: Adjoint Operator; Normal operators; Posinormal operators; Positive operators.


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