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

Research Article · Mathematical Sciences · Volume 2, Issue 9 · Sep 2017 · Pages 318–321

Spectral Characterization of Convexoid Operators

N. B. Okelo, J. A. Otieno, O. Ongati

  • N. B. Okelo: School of Mathematics and Actuarial Science, Jaramogi Oginga Odinga University of Science and Technology, P.O Box 210-40601, Bondo-Kenya.
  • J. A. Otieno: School of Mathematics and Actuarial Science, Jaramogi Oginga Odinga University of Science and Technology, P.O Box 210-40601, Bondo-Kenya.
  • O. Ongati: School of Mathematics and Actuarial Science, Jaramogi Oginga Odinga University of Science and Technology, P.O Box 210-40601, Bondo-Kenya.

Abstract

Spectrum is a very useful property in studying operators on Banach spaces particularly, Hilbert spaces. In particular, the geometrical properties of spectrum often provide useful information about algebraic and analytic properties of an operator. The theory of spectrum played a crucial role in the study of some algebraic structures especially in the associative context. The spectrum of an operator depends strongly upon the base of scalars. Motivated by theoretical study and applications, researchers have considered different generalizations of spectrum. This study gives results of spectrum of convexoid operators. Let H be an infinite dimensional complex Hilbert space and B(H) be algebra of all bounded linear operators on H. T ϵ B(H) is said to be convexoid if the closure of the numerical range coincides with the convex hull of its spectrum. In this paper, the study determines the spectrum of convexoid operators. This work considers some results on spectra due to Rota, Hildebrandant, Furuta and Nakamoto among others.

Keywords

Resolvent set; Convexoid operator; Spectral radius; Spectrum of operator

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