Fine spectrum of the upper triangular matrix U(r, 0, 0, s) over the sequence spaces c0 and c.

• Autores: Binod Chandra Tripathy, Rituparna Das
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 37, Nº. 1, 2018, págs. 85-101
• Idioma: inglés
• DOI: 10.4067/s0716-09172018000100085
• Enlaces
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• Resumen

  • Fine spectra of various matrices have been examined by several authors. In this article we have determined the fine spectrum of the upper triangular matrix U(r, 0, 0, s) on the sequence spaces c0 and c.

• Referencias bibliográficas
  • A. M. Akhmedov and S. R. El-Shabrawy: On the fine spectrum of the operator ∆a,b over the sequence space c, Comput. Math. Appl., 61(10), pp....
  • A. M. Akhmedov and F. Başar: The fine spectra of the Cesàro operator C1 over the sequence space bvp (1 ≤ p < ∞), Math. J. Okayama Univ.,...
  • B. Altay and F. Başar: On the fine spectrum of the difference operator ∆ on c0 and c, Inf. Sci., 168, pp. 217-224, (2004).
  • B. Altay and F. Başar: On the fine spectrum of the generalized difference operator B(r, s) over the sequence spaces c0 and c, Int. J. Math....
  • B. Altay and M. Karakuş: On the spectrum and the fine spectrum of the Zweier matrix as an operator on some sequence spaces, Thai J. Math.,...
  • M. Altun: On the fine spectra of triangular Toeplitz operators, Appl. Math. Comput., 217, pp. 8044-8051, (2011).
  • M. Altun: Fine spectra of tridiagonal symmetric matrices, Int. J. Math. Math. Sci., 2011, Article ID 161209, 10 pages, (2011).
  • F. Başar: Summability Theory and Its Applications, Bentham Science Publishers,e-books, Monographs, Istanbul, 2012, ISBN: 978-1-60805-420-6.
  • H. Bilgiç and H. Furkan: On the fine spectrum of operator B(r, s, t) over the sequence spaces l1 and bv, Math Comput. Model., 45, pp. 883-891,...
  • H. Bilgiç and H.Furkan: On the fine spectrum of the generalized difference operator B(r, s) over the sequence spaces l1 and bvp (1 < p...
  • J. P. Cartlitdge,Weighted mean matrices as operators on lp, Ph.D dissertation,Indiana University,Indiana,(1978).
  • H. Furkan, H. Bilgi¸ c and B. Altay: On the fine spectrum of operator B(r, s, t) over c0 and c, Comput. Math. Appl., 53, pp. 989-998, (2007).
  • S. Goldberg: Unbounded Linear Operators-Theory and Applications, Dover Publications, Inc, New York, (1985).
  • V. Karakaya and M. Altun: Fine spectra of upper triangular doubleband matrices, J. Comp. Appl. Math., 234, pp. 1387-1394, (2010).
  • J. I. Okutoyi: On the spectrum of C1 as an operator on bv0, J. Austral. Math. Soc. (Series A) 48, pp. 79-86, (1990).
  • B. L. Panigrahi and P. D. Srivastava: Spectrum and the fine spectrum of the generalised second order difference operator ∆2uv on sequence...
  • B. L. Panigrahi and P. D. Srivastava: Spectrum and fine spectrum of the generalized second order forward difference operator ∆2uvw on the...
  • B. E. Rhoades: The fine spectra for weighted mean operators, Pac. J. Math., 104(1), pp. 219-230, (1983).
  • P. D. Srivastava and S. Kumar: Fine spectrum of the generalized difference operator ∆v on the sequence space l1, Thai J. Math., 8(2), pp....
  • B. C. Tripathy and R. Das: Spectra of the Rhaly operator on the sequence space bv0 ∩ l∞, Bol. Soc. Parana. Mat., 32(1), pp. 263-275, (2014).
  • B. C. Tripathy and R. Das: Spectrum and fine spectrum of the lower triangular matrix B(r, 0, s) over the sequence space cs, Appl. Math. Inf....
  • B. C. Tripathy and R. Das: Spectrum and fine spectrum of the upper triangular matrix U(r, s) over the sequence space cs, Proyecciones J. Math.,...
  • B. C. Tripathy and A. Paul: Spectra of the operator B(f, g) on the vector valued sequence space c0(X), Bol. Soc. Parana. Mat., 31(1), pp....
  • B. C. Tripathy and A. Paul: Spectrum of the operator D(r, 0, 0, s) over the sequence spaces lp and bvp, Hacet. J. Math. Stat., 43(3), pp....
  • B. C. Tripathy and A. Paul: The spectrum of the operator D(r, 0, 0, s) over the sequence space bv0 , Georgian J. Math., 22(3), pp. 421-426,...
  • B.C. Tripathy and A. Paul: The spectrum of the operator D(r, 0, s, 0, t) over the sequence spaces lp and bvp, Afrika Mat., 26(5-6), pp. 1137-1151,...
  • B. C.Tripathy and A. Paul: The spectrum of the operator D(r, 0, 0, s) over the Sequence Space c0 and c, Kyungpook Math. J., 53 (2), pp. 247-256,...
  • B. C. Tripathy and P. Saikia: On the spectrum of the Cesáro operator C1 on bv ∩ l∞, Math. Slovaca, 63(3), pp. 563-572, (2013).
  • A. Wilansky: Summability Through Functional Analysis, North Holland, 1984.
  • M. Yeşilkayagil and F. Başar: On the fine spectrum of the operator defined by the lambda matrix over the spaces of null and convergent sequences,...