Subdivisions of the Spectra for Difference Operator Δ^m over the Sequence Space l_p

Rabia Kiliç

Subdivisions of the Spectra for Difference Operator Δ^m over the Sequence Space l_p

Abstract

This study focuses on the higher-order difference operator Δ^m, which is defined via an (m+1)-band matrix and serves as a generalization of classical operators such as ∆, Δ^2, B(r,s) and B(r,s,t). Within the framework of the sequence space l_p for 1

Keywords

References

[1] Altay, B., Başar, F., On the fine spectrum of the difference operator on and , Inf. Sci., 168 (2004) 217–224.
[2] Altay, B., Başar, F., The fine spectrum and the matrix domain of the difference operator on the sequence space , , Commun. Math. Anal., 2(2) (2007) 1–11.
[3] Altay, B., Başar, F., On the fine spectrum of the generalized difference operator over the sequence spaces and , Int. J. Math. Math. Sci., 18 (2005) 3005–3013.
[4] Akhmedov, A.M., Başar, F., On the fine spectra of the difference operator over the sequence space , Demonstr. Math., 39(3) (2006) 586–595.
[5] Akhmedov, A.M., Başar, F., On the fine spectra of the difference operator over the sequence space, , Acta. Math. Sin. (Engl. Ser.), 23(10) (2007) 1757–1768.
[6] Durna, N., Yıldırım, M., Kılıç, R., Partition of the spectra for the generalized difference operator on the sequence space , Cumhuriyet Sci. J., 39(1) (2018) 7–15.
[7] Srivastava, P.D., Kumar, S., On the fine spectrum of the generalized difference operator over the sequence space, Commun. Math. Anal., 6(1) (2009) 8–21.
[8] Srivastava, P.D., Kumar, S., Fine spectrum of the generalized difference operator on sequence space , Thai. J. Math., 8(2) (2010) 221–233.

[9] Akhmedov, A.M., El-Shabrawy, S.R., On the fine spectrum of the operator over the sequence space, Comput. Math. Appl., 61 (2011) 2994–3002.
[10] Dutta, S., Baliarsingh, P., On the fine spectra of the generalized difference operator on the sequence space, Appl. Math. Comput., 219 (2012) 1776–1784.
[11] Dutta, S., Baliarsingh, P., On the spectrum of order generalized difference operator over the sequence space , Bol. Soc. Paran. Mat., 31(2) (2013) 235–244.
[12] Durna, N., Yıldırım, M., Ünal, Ç., On the fine spectrum of generalized lower triangular double band matrices Over The Sequence Space, Cumhuriyet Sci. J., 37(3) (2016) 281–291.
[13] Durna, N., Subdivision of spectra for some lower triangular doule-band matrices as operators on , Ukrain. Mat. Zh., 70(7) (2018) 913–922.
[14] Durna, N., Kılıç, R., On the spectrum and fine spectrum of the upper triangular double band matrix over the sequence space , Honam Mathematical J., 45(4) (2023) 598-609.
[15] Durna, N., Mursaleen, M. and Kılıç, R., Spectra and fine spectra of the generalized upper difference operator with triple repetition on the Hahn sequence space, Mathematica Slovaca, 72(3) (2022) 719-736.
[16] Durna, N., Spectra and fine spectra of the upper triangular band matrix on the Hahn sequence space, Mathematical Communications, 25(1) (2020) 49-66.
[17] Rani, J., Patra, A., Srivastava, P. D., Spectrum and Fine Spectrum of Band Matrices Generated by Oscillatory Sequences, Operators and Matrices, 18(4) (2024) 805-831.
[18] Bilgiç, H., Furkan, H., On the fine spectrum of the generalized difference operator over the sequence spaces and , Nonlinear Anal., 68(3) (2008) 499-506.
[19] Furkan, H., Bilgiç, H., Altay, B., On the fine spectrum of the operator over the sequence space and , Comput. Math. Appl., 60(7) (2010) 897–908.
[20] Baliarsingh, P., Mursalen, M., Rakocevic, V., A survey on the spectra of the difference operators over the Banach space , RACSAM, 115(57) (2021) 1–17.
[21] Taylor, R. B., Introduction to functional analysis Wiley, New York, (1980).
[22] Wilansky, A., Summability Through Functional Analysis, North-Holland Mathematics Studies, Amsterdam, (1984).
[23] Goldberg, S., Unbounded Linear Operators, McGraw Hill, New York (1966).
[24] Tuğutlu M., Durna N., On the Spectrum of the difference operator over the sequence space , 1 st ICSAR, Konya, Turkey, 2022,362-366.
[25] Appell, J., Pascale, E.D., Vignoli, A., Nonlinear Spectral Theory, Walter de Gruyter, Berlin New York, (2004).

Details

Primary Language

English

Subjects

Operator Algebras and Functional Analysis

Journal Section

Research Article

Authors

Rabia Kiliç ^*
0000-0002-3415-1945
Türkiye

Publication Date

September 30, 2025

Submission Date

July 26, 2025

Acceptance Date

September 15, 2025

Published in Issue

Year 2025 Volume: 46 Number: 3

IZ

https://izlik.org/JA98PB92UL

Cite

RIS / Bibtex

APA

Kiliç, R. (2025). Subdivisions of the Spectra for Difference Operator Δ^m over the Sequence Space l_p. Cumhuriyet Science Journal, 46(3), 590-594. https://izlik.org/JA98PB92UL