On the spectrum and fine spectrum of an upper triangular double-band matrix on sequence spaces

Document Type : Research Paper

Author

Department of Mathematics, Faculty of Sciences, Fırat University, Elazıvg, Turkey

Abstract

In this paper, we investigate the spectrum and fine spectrum of the upper triangular double-band matrix $\Delta ^{uv}$ on $cs$ sequence space. We also determine the approximate point spectrum, the defect spectrum and the compression spectrum of this matrix on $cs$.

Keywords

[1] A.M. Akhmedov, F. Ba¸sar, On the fine spectra of the difference operator ∆ over the sequence space bvp (1 ≤ p <∞), Acta. Math. Sin. Engl. ser. 23 (2007) 1757-1768.
[2] A.M. Akhmedov, F. Ba¸sar, The fine spectra of the difference operator ∆ over the sequence space `p (1 ≤ p < ∞), Demonstratio Math. 39 (2006) 586-595.
[3] B. Altay, F. Ba¸sar, The fine spectrum and the matrix domain of the difference operator ∆ on the sequence space `p (0 < p < 1), Commun. Math. Anal. 2(2) (2007) 1-11.
[4] J. Appell , E. Pascale, A. Vignoli Nonlinear Spectral Theory, de Gruyter Series in Nonlinear Analysis and Applications 10, Walter de Gruyter, Berlin-New York, 2004.
[5] F. Ba¸sar, B. Altay, On the fine spectrum of the difference operator on c0 and c. Inform. Sci. 168 (2004) 217-224.
[6] S. Dutta , P. Baliarsingh, On the spectrum of difference operator ∆ab over the sequence spaces `p and bvp,( 1 < p < ∞), Math. Sci. Lett. 3(2) (2014) 115-120.
[7] J. Fathi, R. Lashkaripour, On the fine spectra of the generalized forward difference operator ∆v over the sequence space `1, Thai J. Math. 9(3) (2011) 605-617.
[8] J. Fathi, On the fine spectrum of generalized upper triangular double-band matrices ∆uv over the sequence spaces c0 and c, Int. J. Nonlinear Anal. Appl. 7(1) (2016) 31-43.
[9] S. Goldberg, Unbounded Linear Operators Theory and Applications, Dover Publications Inc, New York.
[10] A. Karaisa, Fine spectra of upper triangular double band matrices over the sequence space `p (1 < p < ∞), Discrete Dyn. Nat. Soc. 19 (2012) Article ID 381069.
[11] E. Kreyszig, Introductory Functional Analysis with Applications, John Wiley & Sons Inc., New York, 1989.
[12] B.C. Tripathy, R. Das, Spectrum and fine spectrum of the upper triangular matrix U (r, s) over the sequence space cs,Proyecciones. 34(2) (2015) 107-125.
[13] B.C. Tripathy, R. Das, Spectrum and fine spectrum of lower triangular matrix B (r, 0, s) over the sequence space cs,Appl. Math. Inf. Sci. 9(4) 2015 2139-2145.
Volume 12, Issue 2
November 2021
Pages 163-171
  • Receive Date: 07 June 2019
  • Revise Date: 02 November 2019
  • Accept Date: 04 November 2019