ISSN 2456-0235

International Journal of Modern Science and Technology

INDEXED IN 

​​​​​​​February 2020, Vol. 5, No. 2, pp. 40-44. 

​​Properties of Norm-attainable Classes and Applications to Signal Processing

Benard Okelo, Judith J. E. J Ogal
School 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

Properties of elementary operators have been studied over a long period of time. Such properties include norms, spectrum, positivity, numerical ranges among others. Characterization of elementary operators has been given considerations in different classes. In the present work authors give norm properties of elementary operators in norm-attainable classes. Moreover, we give applications to signal processing.

Keywords: Elementary operators; Norm-attainable classes; Spectrum; Signal Processing.

References

  1. Barraa M, Boumazgour M.  Inner derivation and norm equality. Proc Amer Math Soc 2020;130(7):471-6.  
  2. Halmos PR. A Hilbert Space Problem Book,Springer Verlag New York; 1970.
  3. Lumer G. Semi-inner product spaces. Trans Amer Math Soc 2016;100(5):29-43.  
  4. McIntosh A. Heinz inequalities and perturbation of spectral families. Macquarie Mathematics Reports 2006;291(2):79-86. 
  5. Taylor J. A joint spectrum for several commuting operators. J Funct Anal 2019;6(2):172-91.
  6. Okelo NB. On Characterization of Various Finite Subgroups of Abelian Groups. International Journal of Modern Computation, Information and Communication Technology 2018;1(5):93-8.
  7. Okelo NB. On Normal Intersection Conjugacy Functions in Finite Groups. International Journal of Modern Computation, Information and Communication Technology 2018;1(6):111-5.
  8. Okwany I, Odongo D, and Okelo NB. Characterizations of Finite Semigroups of Multiple Operators. International Journal of Modern Computation, Information and Communication Technology 2018;1(6):116-20.
  9. Ramesh R, Mariappan R. Generalized open sets in Hereditary Generalized Topological Spaces. J Math Comput Sci 2015;5(2):149-59.
  10. Wanjara AO. On the Baire’s Category Theorem as an Important Tool in General Topology and Functional Analysis. International Journal of Modern Computation, Information and Communication Technology 2019;2(4):27-31.