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On the spectrum and fine spectrum of an upper triangular double-band matrix on sequence spaces | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 13، دوره 12، شماره 2، بهمن 2021، صفحه 163-171 اصل مقاله (358.89 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2019.17764.1961 | ||
| نویسنده | ||
| Sinan Ercan* | ||
| Department of Mathematics, Faculty of Sciences, Fırat University, Elazıvg, Turkey | ||
| تاریخ دریافت: 17 خرداد 1398، تاریخ بازنگری: 11 آبان 1398، تاریخ پذیرش: 13 آبان 1398 | ||
| چکیده | ||
| 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 $cs$. | ||
| کلیدواژه‌ها | ||
| Spectrum of an operator؛ sequence space | ||
| مراجع | ||
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[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. | ||
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