Table of Contents
Chinese Journal of Mathematics
Volume 2013, Article ID 286748, 10 pages
http://dx.doi.org/10.1155/2013/286748
Research Article

Some Spectral Aspects of the Operator over the Sequence Spaces and

1Department of Mathematics, Utkal University, Vanivihar, Bhubaneswar 751004, India
2Department of Mathematics, School of Applied Sciences, KIIT University, Bhubaneswar 751024, India

Received 22 July 2013; Accepted 28 August 2013

Academic Editors: Z. Huang, P. K. Sahoo, and W. Sun

Copyright © 2013 S. Dutta and P. Baliarsingh. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. M. Gonzalez, “The fine spectrum of the Cesàro operator in p1LTHEXApLTHEXA,” Archiv der Mathematik, vol. 44, no. 4, pp. 355–358, 1985. View at Publisher · View at Google Scholar · View at Scopus
  2. J. T. Okutoyi, “On the spectrum of C1 as an operator on bv,” Communications de la Faculté des Sciences de l'Université d'Ankara A, vol. 141, pp. 197–207, 1992. View at Google Scholar
  3. A. M. Akhmedov and F. Başar, “The fine spectra of Cesàro operator C1 over the sequence space bvp,” Mathematical Journal of Okayama University, vol. 50, pp. 135–147, 2008. View at Google Scholar
  4. A. M. Akhmedov and F. Başar, “The fine spectra of the difference operator Δ over the sequence space p, 1pLTHEXA,” Demonstratio Mathematica, vol. 39, no. 3, pp. 586–595, 2006. View at Google Scholar
  5. A. M. Akhmedov and F. Başar, “The fine spectra of the difference operator Δ over the sequence space bvp, 1pLTHEXA,” Acta Mathematica Sinica (English Series), vol. 23, no. 10, pp. 1757–1768, 2007. View at Publisher · View at Google Scholar · View at Scopus
  6. B. Altay and F. Başar, “The fine spectrum and the matrix domain of the difference operator Δ on the sequence space p, 0LTHEXApLTHEXA1,” Communications in Mathematical Analysis, vol. 2, pp. 1–11, 2007. View at Google Scholar
  7. K. Kayaduman and H. Furkan, “The fine spectra of the difference operator Δ over the sequence spaces 1 and bv,” International Mathematical Forum, vol. 1, no. 24, pp. 1153–1160, 2006. View at Google Scholar
  8. P. D. Srivastava and S. Kumar, “On the fine spectrum of the generalized difference operator Δν over the sequence space c0,” Communications in Mathematical Analysis, vol. 6, no. 1, pp. 8–21, 2009. View at Google Scholar
  9. S. Dutta and P. Baliarsingh, “On a spectral classification of the operator Δνr over the sequence space c0,” Proceedings of the National Academy of Sciences, India A. In press.
  10. S. Dutta and P. Baliarsingh, “On the fine spectra of the generalized rth difference operator Δνr on the sequence space 1,” Applied Mathematics and Computation, vol. 219, pp. 1776–1784, 2012. View at Google Scholar
  11. B. Altay and F. Başar, “On the fine spectrum of the generalized difference operator Br,s over the sequence spaces c0 and c,” International Journal of Mathematics and Mathematical Sciences, vol. 2005, no. 18, pp. 3005–3013, 2005. View at Publisher · View at Google Scholar · View at Scopus
  12. B. Altay and F. Başar, “On the fine spectrum of the difference operator Δ on c0 and c,” Information Sciences, vol. 168, no. 1–4, pp. 217–224, 2004. View at Publisher · View at Google Scholar · View at Scopus
  13. A. M. Akhmedov and S. R. El-Shabrawy, “On the fine spectrum of the operator Δa,b over the sequence space c,” Computers and Mathematics with Applications, vol. 61, no. 10, pp. 2994–3002, 2011. View at Publisher · View at Google Scholar · View at Scopus
  14. B. L. Panigrahi and P. D. Srivastava, “Spectrum and fine spectrum of generalized second order difference operator Δuν2 on sequence space c0,” Thai Journal of Mathematics, vol. 9, no. 1, pp. 57–74, 2011. View at Google Scholar · View at Scopus
  15. S. Dutta and P. Baliarsingh, “On the spectrum of 2-nd order generalized difference operator Δ2 over the sequence space c0,” Boletim da Sociedade Paranaense de Matemática, vol. 31, no. 2, pp. 235–244, 2013. View at Google Scholar
  16. H. Furkan, H. Bilgiç, and F. Başar, “On the fine spectrum of the operator Br,s,t over the sequence spaces p and bvp, 1pLTHEXA,” Computers and Mathematics with Applications, vol. 60, no. 7, pp. 2141–2152, 2010. View at Publisher · View at Google Scholar · View at Scopus
  17. E. Kreyszig, Introductory Functional Analysis with Applications, John Wiley & Sons, New York, NY, USA, 1978.
  18. S. Goldberg, Unbounded Linear Operators, Dover Publications, New York, NY, USA, 1985.
  19. I. J. Maddox, Elements of Functional Analysis, Cambridge University Press, London, UK, 1970.
  20. B. Choudhary and S. Nanda, Functional Analysis with Applications, John Wiley & Sons, New York, NY, USA, 1989.