Spectrum and Fine Spectrum of the Triple Repetitive Double-Band Matrix Over the Sequence Space $cs$

Rabia Kılıç; Nuh Durna

Research Article

Spectrum and Fine Spectrum of the Triple Repetitive Double-Band Matrix Over the Sequence Space $cs$

Year 2023, Volume: 11 Issue: 2, 97 - 104, 31.10.2023

Rabia Kılıç Nuh Durna

Abstract

The aim of our study is to obtain the spectrum, fine spectrum, approximate point spectrum, defect spectrum and compression spectrum of triple repetitive double-band matrix over the $cs$ sequence space. In addition, the spectrum and fine spectrum of the $n$-repetitive form were investigated in the space of this matrix.

Keywords

band matrix, spectrum, fine spectrum, approximate point spectrum

References

[1] A. M. Akhmedov and F. Bas¸ar, On the fine spectrum of the Ces`aro operator in c0, Math. J. Ibaraki Univ. Vol:36, (2004), 25-32.
[2] A. M. Akhmedov and F. Bas¸ar, The Fine Spectra of the Cesaro Operator C1 over the Sequence Space bvp, (1 p < ¥), Math. J. Okayama University, Vol:50, No.1 (2008), Article 7.
[3] A.M. Akhmedov and S.R. El-Shabrawy, On the fine spectrum of the operator Da;b over the sequence space c, Comput. Math. Appl. Vol:61, No.10 (2011), 2994-3002.
[4] Appell, J., De Pascale, E., and Vignoli, A., Nonlinear Spectral Theory, Walter de Gruyter, Berlin, New York, 2004.
[5] B. Altay and F. Basar, On the fine spectrum of the generalized difference operator B(r; s) over the sequence spaces c0 and c, Int. J. Math. Math. Sci., Vol:18, (2005), 3005-3013.
[6] S. Aydın and H. Polat , Difference sequence spaces derived by using Pascal transform, Fundam. J. Math. Appl., Vol:2, No.1 (2019), 56-62. doi:10.33401/fujma.541721.
[7] H. Bilgic and H. Furkan, On the fine spectrum of the operator B(r; s; t) over the sequence spaces `1 and bv, Math. Comput. Modelling, Vol:45, (2007), 883-891.
[8] M. Candan, A new aspect for some sequence spaces derived using the domain of the matrix ˆB, Fundam. J. Math. Appl., Vol:5, No.1 (2022), 51-62. doi:10.33401/fujma.1003752.
[9] N. Durna, Spectra and fine spectra of the upper triangular band matrix U(a; 0;b) over the sequence space c0, Miskolc Math. Notes, Vol:20, No.1 (2019), 209-223.
[10] N. Durna, Spectra and fine spectra of the upper triangular band matrix U(a; 0;b) on the Hahn sequence space, Math. Commun., Vol:25, No.1 (2020), 49-66.
[11] N. Durna, M. Yildirim and R. Kilic, Partition of the Spectra for the Generalized Difference Operator B(r; s) on the Sequence Space cs, Cumhuriyet Sci. J., Vol:39, No.1 (2018) 7-15.
[12] N. Durna and R. Kilic, Spectra and fine spectra for the upper triangular band matrix U(a0;a1;a2;b0;b1;b2) over the sequence space c0. Proyecciones (Antofagasta), Vol:38, No.1 (2019), 145-162.
[13] S.R. El-Shabrawy, Spectra and fine spectra of certain lower triangular double-band matrices as operators on c0, J. Ineq. App., 2014, (2014), Article number: 241.
[14] S. Ercan, On the spectrum and ne spectrum of an upper triangular double-band matrix on sequence spaces, Int. J. Nonlinear Anal. Appl., Vol:12, No.2 (2021), 163-171.
[15] S. Erdem and S. Demiriz, A study on strongly almost convergent and strongly almost null binomial double sequence spaces, Fundam. J. Math. Appl., Vol:4, No.4 (2021), 271-279. doi:10.33401/fujma.987981.
[16] J. Fathi and R. Lashkaripour, On the fine spectrum of generalized upper double-band matrices Duv over the sequence space `1, Matematiqki Vesnik, Vol:65, No.1 (2013), 64-73.
[17] J. Fathi, On the fine spectrum of generalized upper triangular double-band matrices Duv over the sequence spaces c0 and c, Int. J. Nonlinear Anal. Appl., Vol:7, No.1 (2016), 31-43.
[18] H. Furkan, H. Bilgic and F. Bas¸ar, On the fine spectrum of the operator $B(r, s, t)$ over the sequence spaces `p and bvp, $bv_{p}$, $(1 < p <\infty )$, Comput. Math. Appl., Vol:60, No.7 (2010), 2141-2152.
[19] Goldberg, S., Unbounded Linear Operators, McGraw Hill, New York, 1966.
[20] F. Gökc¸e, Compact and matrix operators on the space $ \left\vert \overline{N}_{p}^{\phi }\right\vert _{k}$, Fundam. J. Math. Appl., Vol:4, No.2 (2021), 124-133. doi:10.33401/fujma.882309.
[21] M. Nur, H. Gunawan, Three equivalent n-norms on the space of p-summable sequences, Fundam. J. Math. Appl., Vol:2, No.2 (2019), 123-129. https://doi.org/10.33401/fujma.635754.
[22] H. Polat, Some new Pascal sequence spaces, Fundam. J. Math. Appl., Vol:1, No.1 (2018), 61-68. doi:10.33401/fujma.409932.
[23] M. Stieglitz and H. Tietz, Matrix tranformationen von Folger¨a umen Eine Ergebnis¨ubersicht, Math. Z., Vol:154, (1977), 1-16.

Year 2023, Volume: 11 Issue: 2, 97 - 104, 31.10.2023

Rabia Kılıç Nuh Durna

Abstract

References

[1] A. M. Akhmedov and F. Bas¸ar, On the fine spectrum of the Ces`aro operator in c0, Math. J. Ibaraki Univ. Vol:36, (2004), 25-32.
[2] A. M. Akhmedov and F. Bas¸ar, The Fine Spectra of the Cesaro Operator C1 over the Sequence Space bvp, (1 p < ¥), Math. J. Okayama University, Vol:50, No.1 (2008), Article 7.
[3] A.M. Akhmedov and S.R. El-Shabrawy, On the fine spectrum of the operator Da;b over the sequence space c, Comput. Math. Appl. Vol:61, No.10 (2011), 2994-3002.
[4] Appell, J., De Pascale, E., and Vignoli, A., Nonlinear Spectral Theory, Walter de Gruyter, Berlin, New York, 2004.
[5] B. Altay and F. Basar, On the fine spectrum of the generalized difference operator B(r; s) over the sequence spaces c0 and c, Int. J. Math. Math. Sci., Vol:18, (2005), 3005-3013.
[6] S. Aydın and H. Polat , Difference sequence spaces derived by using Pascal transform, Fundam. J. Math. Appl., Vol:2, No.1 (2019), 56-62. doi:10.33401/fujma.541721.
[7] H. Bilgic and H. Furkan, On the fine spectrum of the operator B(r; s; t) over the sequence spaces `1 and bv, Math. Comput. Modelling, Vol:45, (2007), 883-891.
[8] M. Candan, A new aspect for some sequence spaces derived using the domain of the matrix ˆB, Fundam. J. Math. Appl., Vol:5, No.1 (2022), 51-62. doi:10.33401/fujma.1003752.
[9] N. Durna, Spectra and fine spectra of the upper triangular band matrix U(a; 0;b) over the sequence space c0, Miskolc Math. Notes, Vol:20, No.1 (2019), 209-223.
[10] N. Durna, Spectra and fine spectra of the upper triangular band matrix U(a; 0;b) on the Hahn sequence space, Math. Commun., Vol:25, No.1 (2020), 49-66.
[11] N. Durna, M. Yildirim and R. Kilic, Partition of the Spectra for the Generalized Difference Operator B(r; s) on the Sequence Space cs, Cumhuriyet Sci. J., Vol:39, No.1 (2018) 7-15.
[12] N. Durna and R. Kilic, Spectra and fine spectra for the upper triangular band matrix U(a0;a1;a2;b0;b1;b2) over the sequence space c0. Proyecciones (Antofagasta), Vol:38, No.1 (2019), 145-162.
[13] S.R. El-Shabrawy, Spectra and fine spectra of certain lower triangular double-band matrices as operators on c0, J. Ineq. App., 2014, (2014), Article number: 241.
[14] S. Ercan, On the spectrum and ne spectrum of an upper triangular double-band matrix on sequence spaces, Int. J. Nonlinear Anal. Appl., Vol:12, No.2 (2021), 163-171.
[15] S. Erdem and S. Demiriz, A study on strongly almost convergent and strongly almost null binomial double sequence spaces, Fundam. J. Math. Appl., Vol:4, No.4 (2021), 271-279. doi:10.33401/fujma.987981.
[16] J. Fathi and R. Lashkaripour, On the fine spectrum of generalized upper double-band matrices Duv over the sequence space `1, Matematiqki Vesnik, Vol:65, No.1 (2013), 64-73.
[17] J. Fathi, On the fine spectrum of generalized upper triangular double-band matrices Duv over the sequence spaces c0 and c, Int. J. Nonlinear Anal. Appl., Vol:7, No.1 (2016), 31-43.
[18] H. Furkan, H. Bilgic and F. Bas¸ar, On the fine spectrum of the operator $B(r, s, t)$ over the sequence spaces `p and bvp, $bv_{p}$, $(1 < p <\infty )$, Comput. Math. Appl., Vol:60, No.7 (2010), 2141-2152.
[19] Goldberg, S., Unbounded Linear Operators, McGraw Hill, New York, 1966.
[20] F. Gökc¸e, Compact and matrix operators on the space $ \left\vert \overline{N}_{p}^{\phi }\right\vert _{k}$, Fundam. J. Math. Appl., Vol:4, No.2 (2021), 124-133. doi:10.33401/fujma.882309.
[21] M. Nur, H. Gunawan, Three equivalent n-norms on the space of p-summable sequences, Fundam. J. Math. Appl., Vol:2, No.2 (2019), 123-129. https://doi.org/10.33401/fujma.635754.
[22] H. Polat, Some new Pascal sequence spaces, Fundam. J. Math. Appl., Vol:1, No.1 (2018), 61-68. doi:10.33401/fujma.409932.
[23] M. Stieglitz and H. Tietz, Matrix tranformationen von Folger¨a umen Eine Ergebnis¨ubersicht, Math. Z., Vol:154, (1977), 1-16.

There are 23 citations in total.

Details

Primary Language	English
Subjects	Mathematical Sciences
Journal Section	Articles
Authors	Rabia Kılıç 0000-0002-3415-1945 Nuh Durna
Publication Date	October 31, 2023
Submission Date	September 26, 2022
Acceptance Date	September 29, 2023
Published in Issue	Year 2023 Volume: 11 Issue: 2

Cite

APA	Kılıç, R., & Durna, N. (2023). Spectrum and Fine Spectrum of the Triple Repetitive Double-Band Matrix Over the Sequence Space $cs$. Konuralp Journal of Mathematics, 11(2), 97-104.
AMA	Kılıç R, Durna N. Spectrum and Fine Spectrum of the Triple Repetitive Double-Band Matrix Over the Sequence Space $cs$. Konuralp J. Math. October 2023;11(2):97-104.
Chicago	Kılıç, Rabia, and Nuh Durna. “Spectrum and Fine Spectrum of the Triple Repetitive Double-Band Matrix Over the Sequence Space $cs$”. Konuralp Journal of Mathematics 11, no. 2 (October 2023): 97-104.
EndNote	Kılıç R, Durna N (October 1, 2023) Spectrum and Fine Spectrum of the Triple Repetitive Double-Band Matrix Over the Sequence Space $cs$. Konuralp Journal of Mathematics 11 2 97–104.
IEEE	R. Kılıç and N. Durna, “Spectrum and Fine Spectrum of the Triple Repetitive Double-Band Matrix Over the Sequence Space $cs$”, Konuralp J. Math., vol. 11, no. 2, pp. 97–104, 2023.
ISNAD	Kılıç, Rabia - Durna, Nuh. “Spectrum and Fine Spectrum of the Triple Repetitive Double-Band Matrix Over the Sequence Space $cs$”. Konuralp Journal of Mathematics 11/2 (October 2023), 97-104.
JAMA	Kılıç R, Durna N. Spectrum and Fine Spectrum of the Triple Repetitive Double-Band Matrix Over the Sequence Space $cs$. Konuralp J. Math. 2023;11:97–104.
MLA	Kılıç, Rabia and Nuh Durna. “Spectrum and Fine Spectrum of the Triple Repetitive Double-Band Matrix Over the Sequence Space $cs$”. Konuralp Journal of Mathematics, vol. 11, no. 2, 2023, pp. 97-104.
Vancouver	Kılıç R, Durna N. Spectrum and Fine Spectrum of the Triple Repetitive Double-Band Matrix Over the Sequence Space $cs$. Konuralp J. Math. 2023;11(2):97-104.

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