​​​​​International Journal of Modern Science and Technology, Vol. 2, No. 7, 2017, Pages 273-276. 

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​Characterization of Spectra of Posinormal Operators  

S. Asamba¹, N. B. Okelo²,*, R. K. Obogi¹
¹Department of Mathematics, Kisii University, P.O. Box 408-40200, Kisii. Kenya.
²School 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 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.

​References

  1. Andrew A. and Green W. Spectral theory of operators on Hilbert space, School of mathematics. Georgia Institute of Technology. Atlanta; 2002.
  2. Chinnadurai V, Bharathivelan K. Cubic Ideals in Near Subtraction Semigroups. International Journal of Modern Science and Technology. 2016;1(8):276-282.
  3. Cho M. Spectral properties of p-Hyponormal operators. Glasgow Math J. 1994;(36):117-122.
  4. Cho M. and Takaguchi M., Some classes of commuting n-tuples of operators. Studia Math. 1984: (80)246-259.
  5. Halmos P. A Hibert space problem book. Van Nostrand, Princenton, 1967.
  6. Itoh M. Characterization of posinormal operators. Nihonkai Math J.  1994;(11):97-101.
  7. Judith JO, Okelo NB, Roy K, Onyango T. Numerical Solutions of Mathematical Model on Effects of Biological Control on Cereal Aphid Population Dynamics. International Journal of Modern Science and Technology. 2016;1(4):138-143.
  8. Judith JO, Okelo NB, Roy K, Onyango T. Construction and Qualitative Analysis of Mathematical Model for Biological Control on Cereal Aphid Population Dynamics. International Journal of Modern Science and Technology. 2016:;1(5):150-158.
  9. Lankham I. The Spectral Theorem for normal linear maps. University of California, Davis; 2007.
  10. Okelo B. A survey of development in operator theory on various classes of operators with applications in quantum mechanics. JP and A Sci. and Tech. 2011; (1) :1-9.
  11. Okelo B, Kisengo S. On the numerical range and spectrum of normal operators on Hilbrt spaces. The SciTech Journal of Science and Technology. 2012L(6):S59-65.
  12. Rhaly H. Posinormal Operators. J Math Soc Japan. 1994;(46):587-605.
  13. Vijayabalaji S, Shyamsundar G. Interval-valued intuitionistic fuzzy transition matrices. International Journal of Modern Science and Technology. 2016;1(2):47-51.
  14. Vijayabalaji S, Sathiyaseelan N. Interval-Valued Product Fuzzy Soft Matrices and its Application in Decision Making. International Journal of Modern Science and Technology. 2016;1(6):159-163.
  15. Xia D. Spectral theory of hyponormal operators. Birhauser Verlag, Basel: 1983.

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International Journal of Modern Science and Technology