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

Research Article · Mathematical Sciences · Volume 2, Issue 7 · Jul 2017 · Pages 273–276

Characterization of Spectra of Posinormal Operators

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

  • S. Asamba: 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
  • R. K. Obogi: Department of Mathematics, Kisii University, P.O. Box 408-40200, Kisii. Kenya.

Abstract

Let H be a complex Hilbert space equipped with the inner product and let B(H) be the algebra of bounded linear operators acting on H. In this paper we have investigated the spectrum of an operator acting on a complex Hilbert space. In particular, we characterized the spectrum of a posinormal operator on an infinite dimensional complex Hilbert space. We also considered the point spectrum, the approximate point spectrum of a posinormal operator A and doubly commuting n-tuples of posinormal operators acting on a complex Hilbert space H. We have shown that Xia’s property holds for a posinormal operator A. Finally, we have proved that doubly commuting n-tuples of posinormal operators are jointly normaloid.

Keywords

Spectrum; Posinormal operator; Hilbert Space; Spectral radius

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