Advertisement

Ukrainian Mathematical Journal

, Volume 70, Issue 7, pp 1052–1062 | Cite as

Subdivision of Spectra for Some Lower Triangular Double-Band Matrices as Operators on c0

  • N. Durna
Article
  • 8 Downloads
The generalized difference operator ∆a,b was defined by El-Shabrawy:
$$ {\varDelta}_{a,b}x={\varDelta}_{a,b}\left({x}_n\right)={\left({a}_n{x}_n+{b}_{n-1}\right)}_{n=0}^{\infty}\;\mathrm{with}\;{x}_{-1}={b}_{-1}=0, $$
where (ak) and (bk) are convergent sequences of nonzero real numbers satisfying certain conditions. We completely determine the approximate point spectrum, the defect spectrum, and the compression spectrum of the operator ∆a,b in a sequence space c0.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    A. M. Akhmedov and El-S. R. Shabrawy, “The spectrum of the generalized lower triangle double-band matrix ∆a over the sequence space c,” Al-Azhar Univ. Eng. J. (Special Issue), 5, No. 9, 54–63 (2010).Google Scholar
  2. 2.
    A. M. Akhmedov and El-S. R. Shabrawy, “On the fine spectrum of the operator ∆v over the sequence space c and p (1 < p < ∞),Appl. Math. Inform. Sci., 5, No. 3, 635–654 (2011).MathSciNetGoogle Scholar
  3. 3.
    B. Altay and F. Bașar, “On the fine spectrum of the difference operator on c 0 and c,” Inform. Sci., 168, 217–224 (2004).MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    J. Appell, E. D. Pascale, and A. Vignoli, Nonlinear Spectral Theory, De Gruyter, Berlin; New York (2004).zbMATHCrossRefGoogle Scholar
  5. 5.
    F. Bașar, N. Durna, and M. Yildirim, “Subdivisions of the spectra for generalized difference operator ∆v on the sequence space 1,” Int. Conf. Math. Sci., 254–260 (2010).Google Scholar
  6. 6.
    F. Bașar, N. Durna, and M. Yildirim, “Subdivisions of the spectra for generalized difference operator over certain sequence spaces,” J. Thai J. Math., 9, No. 2, 285–295 (2011).MathSciNetzbMATHGoogle Scholar
  7. 7.
    F. Bașar, N. Durna, and M. Yildirim, “Subdivision of the spectra for difference operator over certain sequence spaces,” Malays. J. Math. Sci., 6, 151–165 (2012).MathSciNetzbMATHGoogle Scholar
  8. 8.
    N. Durna and M. Yildirim, “Subdivision of the spectra for factorable matrices on c 0,” GUJ Sci., 24, No. 1, 45–49 (2011).zbMATHGoogle Scholar
  9. 9.
    S. R. El-Shabrawy, “On the fine spectrum of the generalized difference operator ∆a,b over the sequence space p (1 < p < ∞),Appl. Math. Inform. Sci., 6, No. 1, 111–118 (2012).MathSciNetzbMATHGoogle Scholar
  10. 10.
    S. R. El-Shabrawy, “Spectra and fine spectra of certain lower triangular double band matrices as operators on c 0,” J. Inequal. Appl., 241, No. 1, 1–9 (2014).MathSciNetzbMATHGoogle Scholar
  11. 11.
    J. Fathi and R. Lashkaripour, “On the fine spectra of the generalized difference operator ∆uv over the sequence space c 0,” J. Mahani Math. Res. Cent., 1, No. 1, 1–12 (2012).zbMATHGoogle Scholar
  12. 12.
    S. Goldberg, Unbounded Linear Operators, McGraw Hill, New York (1966).zbMATHGoogle Scholar
  13. 13.
    M. Gonzalez, “The fine spectrum of the Cesaro operator in p (1 < p < ∞),Arch. Math. (Basel), 44, 355–358 (1985).MathSciNetzbMATHCrossRefGoogle Scholar
  14. 14.
    K. Kayaduman and H. Furkan, “On the fine spectrum of the difference operator ∆ over the sequence spaces 1 and bv,” Int. Math. Forum, 24, No. 1, 1153–1160 (2006).zbMATHCrossRefGoogle Scholar
  15. 15.
    J. B. Reade, “On the spectrum of the Cesaro operator,” Bull. Lond. Math. Soc., 17, 263–267 (1985).MathSciNetzbMATHCrossRefGoogle Scholar
  16. 16.
    B. E. Rhoades, “The fine spectra for weighted mean operators,” Pacific J. Math., 104, 263–267 (1983).MathSciNetzbMATHCrossRefGoogle Scholar
  17. 17.
    M. Yildirim, “On the spectrum of the Rhaly operators on c 0 and c,” Indian J. Pure Appl. Math., 29, 1301–1309 (1998).MathSciNetzbMATHGoogle Scholar
  18. 18.
    M. Yildirim, “The fine spectra of the Rhaly operators on c 0,” Turkish J. Math., 26, No. 3, 273–282 (2002).MathSciNetzbMATHGoogle Scholar
  19. 19.
    R. B. Wenger, “The fine spectra of H¨older summability operators,” Indian J. Pure Appl. Math., 6, 695–712 (1975).MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • N. Durna
    • 1
  1. 1.Cumhuriyet UniversitySivasTurkey

Personalised recommendations