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

Research Article · Mathematical Sciences · Volume 3, Issue 2 · Feb 2018 · Pages 27–32

Necessary and Sufficient conditions for Normality of Operators in Hilbert spaces

A. M. Wafula, N. B. Okelo, O. Ongati

  • A. M. Wafula: School of Mathematics and Actuarial Science, Jaramogi Oginga Odinga University of Science and Technology, P.O. Box 2010-40601, Bondo-Kenya.
  • N. B. Okelo: School of Mathematics and Actuarial Science, Jaramogi Oginga Odinga University of Science and Technology, P.O. Box 2010-40601, Bondo-Kenya.
  • O. Ongati: School of Mathematics and Actuarial Science, Jaramogi Oginga Odinga University of Science and Technology, P.O. Box 2010-40601, Bondo-Kenya.

Abstract

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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