ISSN 2581-5954

July 2019, Vol. 2, Issue 7, p. 53-58.​​

On spectra of n-hyponormal operators in Hilbert space
M. E. O. Wegulo¹, S. Aywa¹, N. B. Okelo²
¹Department of Mathematics, Kibabii University, Kenya.
²Department of Pure and Applied Mathematics, Jaramogi Oginga Odinga University of Science and TechnologyP. O. Box 210 - 40601, Bondo-Kenya.
*Corresponding author’s e-mail:
bnyaare@yahoo.com

Abstract

Many practical applications of Mathematics rely on results in operator theory. In this paper we focus on the characterization of the spectrum of a hyponormal operator and the spectrum of its adjoint. Considering an atomic quantum mechanical system, if A is an operator of an atom, then the differences of the various eigenvalues of A are the amounts of energy emitted by the atom as it undergoes transitions. These amounts are seen in the form of electromagnetic waves, which constitute the optical spectrum of the report. The main objective will be finding a formal evaluation of the spectra of hyponormals and the spectrum of its adjoint. Emphasis will also be on the resultant spectra of similar operators to find any relationships.

Keywords: Operator; n-Power-hyponormal; Eigenvalues; Eigenvectors; Conjugates; Transpose; Adjoint; Spectrum.

References

  1. Aluthge A. Integral and Operator Theory. Springer Verlag, New York; 2017.
  2. Berberian S. Introduction to Hilbert Space. Oxford University Press, New York; 2018.
  3. Brian D. Linear Operators and their Spectra. Cambridge University Press, 2007.
  4. Halmos P. A Hilbert Space Problem Book. Van Nostrand, Princeton; 1967.
  5. Rimaye BV.  Functional Analysis. Wiley Eastern, New Delhi; 1981.
  6. Stampi J. Which weighted shifts are hyponormal. Pacific J Math 1966:17(3):67-79.
  7. Xia D. Spectral theory of hyponormal operators. Birkhauser Verlag, Basel; 2013.
  8. Okelo NB. Certain properties of Hilbert space operators. Int J Mod Sci Technol 2018;3(6):126-32.
  9. Okelo NB. Certain Aspects of Normal Classes of Hilbert Space Operators/ Int J Mod Sci Technol 2018;3(10):203-7.
  10. Okelo NB. Characterization of Numbers using Methods of Staircase and Modified Detachment of Coefficients. Int J Mod Comp Info and Com Technol 2018;1(4):88-92.
  11. Okelo NB. On Characterization of Various Finite Subgroups of Abelian Groups. Int J Mod Comput Info and Commun Technol 2018;1(5):93-8.
  12. Okelo NB. On Normal Intersection Conjugacy Functions in Finite Groups. Int J Mod Comput Info and Commun Technol 2018; 1(6): 111-115.
  13. Okwany I, Odongo D, and Okelo NB. Characterizations of Finite Semigroups of Multiple Operators. Int J Mod Comput Info and Commun Technol 2018;1(6):116-20.
  14. Ramesh R, Mariappan R. Generalized open sets in Hereditary Generalized Topological Spaces/ J B Math Comput Sci 2015;5(2):149-59.
  15. Vijayabalaji S, Sathiyaseelan N. Interval Valued Product Fuzzy Soft Matrices and its Application in Decision Making. Int J Mod Sci Technol 2016;1(7):159-63.
  16. Wanjara AO, Okelo NB, Ongati O. On Characterization of Very Rotund Banach Spaces. Int J Mod Comput Info and Commun Technol 2018;1(5):99-102.
LATEST NEWS

International Journal of Modern Computation, Information and Communication Technology