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Year 2021, , 677 - 687, 24.09.2021

Nuh Durna , Mustafa Yıldırım , Abbas Kılıç

https://doi.org/10.17776/csj.884643

Abstract

References

  • [1] Amirov R. Kh., Durna N., Yildirim M., Subdivisions of the spectra for cesaro, rhaly and weighted mean operators on c_0,c and l_p, IJST, A3 (2011) 175-183.
  • [2]Appell J., Pascale E.D, Vignoli A., Nonlinear Spectral Theory, Berlin, New York: Walter de Gruyter, (2002).
  • [3]Stone M.H., Linear transformations in Hilbert space and their applications to analysis, New York (NY): American Mathematical Society; 1932.
  • [4]Goldberg S., Unbounded Linear Operators, New York:McGraw Hill, (1966).
  • [5]Brown A., Halmos P.R., Shields A.L., Cesàro operators, Acta Sci. Math. (Szeged) 26(1-2) (1965) 125-137.
  • [6]Cass, F.P.; Rhoades, B. E., Mercerian theorems via spectral theory, Pacific J. Math. 73(1) (1977) 63-71.
  • [7] Cartlidge J.P., Weighted Mean Matrices as Operator on l_p, Ph.D. Dissertation, Indiana University, 1978.
  • [8]Başar F., Durna N., Yildirim M., Subdivisions of the Spectra for Generalized Difference Operator over Certain Sequence Spaces, Thai J. Math. 9(2) (2011), 285-295.
  • [9]Durna N, Yıldırım M., Subdivision of the spectra for factorable matrices on c_0, GUJ Sci, 24(1) (2011) 45-49.
  • [10] Durna N, Yıldırım M., Subdivision of the spectra for factorable matrices on c and l_p, Math. Commun., 16 (2011) 519-530.
  • [11] Durna, N. , Yıldırım, M., Kılıç, R., Partition of the Spectra for the Generalized Difference Operator B(r,s) on the Sequence Space cs,. Cumhuriyet Sci. J., 39 (1) (2018), 7-15.
  • [12] Akhmedov A.M., El-Shabrawy S.R., Spectra and Fine Spectra of Lower Triangular Double-Band Matrices as Operators on L_p (1≤p<∞), Mathematica Slovaca 65(5) (2015) 1137-1152.
  • [13] Bilgiç H., Furkan H., On the fine spectrum of the generalized difference operator B(r,s) over the sequence spaces l_p and 〖bv〗_p (1<p<∞), Nonlinear Anal. 68(3) (2008) 499-506.
  • [14] Coskun C., The spectra and fine spectra for p-Cesàro operators, Turkish J. Math., 21 (1997) 207-212.
  • [15] Das R., On the spectrum and fine spectrum of the lower triangular matrix B(±r,±s) over the sequence space c_0, International Journal of Mathematical Archive 6(1) (2015) 229-240.
  • [16] Das R., On The fine spectra of the lower triangular matrix Δ(r,s) over the sequence space l_1, Internat. J. Functional Analysis, Operator Theory and Applications, 7(1) (2015) 1-18.
  • [17] Fathi J., On the ne spectrum of generalized upper triangular double-band matrices uv over the sequence spaces c_0 and c, Int. J. Nonlinear Anal. Appl, 7(1) (2015) 31-43.
  • [18] Karakaya V., Manafov M., Şimşek N., On the fine spectrum of the second order difference operator over the sequence spaces〖 l〗_p and 〖bv〗_p (1<p<∞), Mathematical and Computer Modelling 55(3-4) (2012) 426-431.
  • [19] Rhoades B.E, Yıldırım M., Spectra and fine spectra for factorable matrices, Integr.Equ. Oper. Theory, 53 (2005) 127-144.
  • [20] El-Shabrawy S.R., Spectra and fine spectra of certain lower triangular double-band matrices as operators on c_0, J. Inequal. Appl., 2014 (2014) 1-9.
  • [21] Srivastava P.D., Kumar S., Fine spectrum of the generalized difference operator Δ_uv on sequence space 〖 l〗_1, Appl. Math. Comput., 218(11) (2012) 6407-6414.
  • [22] Tripathy B.C., Das R., Spectrum and fine spectrum of the upper triangular matrix U(r,s) over the sequence space cs, Proyecciones Journal of Mathematics 34(2) (2015) 107-125.
  • [23] Tripathy B.C., Das R., Spectrum and fine spectrum of the lower triangular matrix B(r,0,s) over the sequence space cs, Appl. Math. Inf. Sci. 9(4) (2015) 2139-2145.
  • [24] Yıldırım M., On the spectrum and fine spectrum of the compact Rhally operators, Indian J. Pure Appl. Math.,27(8) (1996) 779-784.
  • [25] Yıldırım M.E., The spectrum and fine spectrum of q-Cesaro matrices with 0<q<1 on c_0, Numerical functional analysis and optimization, 41(3) (2020) 361-377.
  • [26] Wilansky A., Summability through Functional Analysis, vol. 85 of North-Holland Mathematics Studies, North-Holland, The Netherlands, Amsterdam 1984.
  • [27] Altun M., Fine Spectra of Tridiagonal Symmetric Matrices, International Journal of Mathematics and Mathematical Sciences (2011) 161209

On the fine spectra of the Jacobi matrices on c_0,c,l_p (1≤p≤∞) and 〖bv〗_p (1≤p<∞)

Year 2021, , 677 - 687, 24.09.2021

Nuh Durna , Mustafa Yıldırım , Abbas Kılıç

https://doi.org/10.17776/csj.884643

Abstract

The spectrum and spectral divisions of band matrices are very new and popular topics of studies. In this paper, our aims are to investigate boundedness of Jacobi matrix which is a band matrix has important role in physics and give subdivisions of the spectra, which are approximate point spectrum, defect spectrum and compression spectrum, for a special type Jacobi matrix. Moreover, we will find the fine division of spectrum which is given by Goldberg with the help of it.

Keywords

Jacobi matrices Spectrum Fine spectrum

References

  • [1] Amirov R. Kh., Durna N., Yildirim M., Subdivisions of the spectra for cesaro, rhaly and weighted mean operators on c_0,c and l_p, IJST, A3 (2011) 175-183.
  • [2]Appell J., Pascale E.D, Vignoli A., Nonlinear Spectral Theory, Berlin, New York: Walter de Gruyter, (2002).
  • [3]Stone M.H., Linear transformations in Hilbert space and their applications to analysis, New York (NY): American Mathematical Society; 1932.
  • [4]Goldberg S., Unbounded Linear Operators, New York:McGraw Hill, (1966).
  • [5]Brown A., Halmos P.R., Shields A.L., Cesàro operators, Acta Sci. Math. (Szeged) 26(1-2) (1965) 125-137.
  • [6]Cass, F.P.; Rhoades, B. E., Mercerian theorems via spectral theory, Pacific J. Math. 73(1) (1977) 63-71.
  • [7] Cartlidge J.P., Weighted Mean Matrices as Operator on l_p, Ph.D. Dissertation, Indiana University, 1978.
  • [8]Başar F., Durna N., Yildirim M., Subdivisions of the Spectra for Generalized Difference Operator over Certain Sequence Spaces, Thai J. Math. 9(2) (2011), 285-295.
  • [9]Durna N, Yıldırım M., Subdivision of the spectra for factorable matrices on c_0, GUJ Sci, 24(1) (2011) 45-49.
  • [10] Durna N, Yıldırım M., Subdivision of the spectra for factorable matrices on c and l_p, Math. Commun., 16 (2011) 519-530.
  • [11] Durna, N. , Yıldırım, M., Kılıç, R., Partition of the Spectra for the Generalized Difference Operator B(r,s) on the Sequence Space cs,. Cumhuriyet Sci. J., 39 (1) (2018), 7-15.
  • [12] Akhmedov A.M., El-Shabrawy S.R., Spectra and Fine Spectra of Lower Triangular Double-Band Matrices as Operators on L_p (1≤p<∞), Mathematica Slovaca 65(5) (2015) 1137-1152.
  • [13] Bilgiç H., Furkan H., On the fine spectrum of the generalized difference operator B(r,s) over the sequence spaces l_p and 〖bv〗_p (1<p<∞), Nonlinear Anal. 68(3) (2008) 499-506.
  • [14] Coskun C., The spectra and fine spectra for p-Cesàro operators, Turkish J. Math., 21 (1997) 207-212.
  • [15] Das R., On the spectrum and fine spectrum of the lower triangular matrix B(±r,±s) over the sequence space c_0, International Journal of Mathematical Archive 6(1) (2015) 229-240.
  • [16] Das R., On The fine spectra of the lower triangular matrix Δ(r,s) over the sequence space l_1, Internat. J. Functional Analysis, Operator Theory and Applications, 7(1) (2015) 1-18.
  • [17] Fathi J., On the ne spectrum of generalized upper triangular double-band matrices uv over the sequence spaces c_0 and c, Int. J. Nonlinear Anal. Appl, 7(1) (2015) 31-43.
  • [18] Karakaya V., Manafov M., Şimşek N., On the fine spectrum of the second order difference operator over the sequence spaces〖 l〗_p and 〖bv〗_p (1<p<∞), Mathematical and Computer Modelling 55(3-4) (2012) 426-431.
  • [19] Rhoades B.E, Yıldırım M., Spectra and fine spectra for factorable matrices, Integr.Equ. Oper. Theory, 53 (2005) 127-144.
  • [20] El-Shabrawy S.R., Spectra and fine spectra of certain lower triangular double-band matrices as operators on c_0, J. Inequal. Appl., 2014 (2014) 1-9.
  • [21] Srivastava P.D., Kumar S., Fine spectrum of the generalized difference operator Δ_uv on sequence space 〖 l〗_1, Appl. Math. Comput., 218(11) (2012) 6407-6414.
  • [22] Tripathy B.C., Das R., Spectrum and fine spectrum of the upper triangular matrix U(r,s) over the sequence space cs, Proyecciones Journal of Mathematics 34(2) (2015) 107-125.
  • [23] Tripathy B.C., Das R., Spectrum and fine spectrum of the lower triangular matrix B(r,0,s) over the sequence space cs, Appl. Math. Inf. Sci. 9(4) (2015) 2139-2145.
  • [24] Yıldırım M., On the spectrum and fine spectrum of the compact Rhally operators, Indian J. Pure Appl. Math.,27(8) (1996) 779-784.
  • [25] Yıldırım M.E., The spectrum and fine spectrum of q-Cesaro matrices with 0<q<1 on c_0, Numerical functional analysis and optimization, 41(3) (2020) 361-377.
  • [26] Wilansky A., Summability through Functional Analysis, vol. 85 of North-Holland Mathematics Studies, North-Holland, The Netherlands, Amsterdam 1984.
  • [27] Altun M., Fine Spectra of Tridiagonal Symmetric Matrices, International Journal of Mathematics and Mathematical Sciences (2011) 161209
There are 27 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Natural Sciences
Authors

Nuh Durna 0000-0001-5469-7745

Mustafa Yıldırım 0000-0002-8880-5457

Abbas Kılıç 0000-0002-5487-6556

Publication Date September 24, 2021
Submission Date February 22, 2021
Acceptance Date August 10, 2021
Published in Issue Year 2021

Cite

APA Durna, N., Yıldırım, M., & Kılıç, A. (2021). On the fine spectra of the Jacobi matrices on c_0,c,l_p (1≤p≤∞) and 〖bv〗_p (1≤p<∞). Cumhuriyet Science Journal, 42(3), 677-687. https://doi.org/10.17776/csj.884643