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Characteristic Numbers of Upper Triangular One-Band Block Operator Matrices

Yıl 2018, Cilt: 10, 173 - 177, 29.12.2018

Rukiye Öztürk Mert Pembe İpek Al Zameddin I. Ismailov

Öz

In this work the boundedness and compactness properties of upper triangular one-band
block operator matrices in the innite direct sum of Hilbert spaces have been studied. We also obtain
the necessary and sucient conditions when these operators belong to Schatten-von Neumann classes.

Anahtar Kelimeler

Direct sum of Hilbert spaces Upper triangular one-band block operator matrix Compact operator

Kaynakça

  • Akhmedov, A. M., El-Shabrawy, S. R., On the Spectrum of the Generalized Lower Triangle Double-Band Matrices , Lviv, (2010), 17-21.
  • Akhmedov, A. M., El-Shabrawy, S. R., Notes on the Spectrum of Lower Triangular Double-Band Matrices , Thai Journal of Mathematics, 10(2012), 415-421.
  • Baliarsingh, P., Dutta, S., On a Spectral Classi cation of the operator r v Over the Sequence Space c0 , Proc. Math. Acad. Sci. India, Sect. A Phys., 84, 4(2014), 555-561.
  • Başar, F., Karaisa, A., Spectrum and Fine Spectrum of the Generalized Difference Operator De ned by Double Sequential Upper Band Matrix Over the Sequence Spaces lp; (1 < p < 1); Hacet. J. Math., 44, 6(2015), 1315-1332.
  • Böttcher, A., Silbermann, B., Analysis of Teoplitz Operators, Berlin, Springer-Verlag, 1990.
  • Böttcher, A., Grudsky, S., Toeplitz Matrices, Asymptotic Linear Algebra anf Functional Analysis, Berlin, Springer-Verlag, 1991.
  • Dunford, N., Schwartz, J. T., Linear Operators I, II, Second ed., Interscience, New York, 1958; 1963.
  • El-Shabrawy, S. R., Spectra and Fine Spectra of Certain Lower Triangular Double-Band Matrices as Operator on c0 , Journal of Inequalities and Applications, 241, 1(2014), 2-9.
  • Gohberg, I., Goldberg, S., Kaashock, M. A., Basic Classes of Linear Operators, Springer, 1990.
  • Ismailov, Z. I., Otkun Çevik, E., Unluyol, E., Compact Inverses of Multipoint Normal Differential Operators for First Order , Electronic Journal of Differential Equations, 89(2011), 1-11.
  • Jeribi, A., Spectral Theory and Applications of Linear Operators and Block Operator Matrices, Springer, 2015.
  • Karakaya, V., Dzh. Manafov, M., Simsek, N., On the Fine Spectrum of the Second Order Di erence Operator Over the Sequence Spaces lp and bvp; (1 < p < 1) , Mathematical and Computer Modelling, 55(2012), 426-431.
  • Kochubei, A. N., Symmetric Operators and Nonclassical Spectral Problems , Mat. Zametki, 25, 3(1979), 425-434.
  • Langer, M., Strauss, M., Spectral Properties of Unbounded j􀀀Self Adjoint Block Operator Matrices , arXiv:1410.1213 [math.SP], 1-37.
  • Nagel, R. , The Spectrum of Unbounded Operator Matrices with Non-Diagonal Domain, Journal of Functional Analysis , 89(1990), 291-302.
  • Otkun Çevik, E., Ismailov, Z. I., Spectrum of the Direct Sum of Operators, Electronic Journal of Differential Equations , 210(2012), 1-8.
  • Tretter, Ch., Spectral Theory of Block Operator Matrices and Applications, Londan: Imperial CollegePress, 264p, 2008.
  • Tripathy, B. C., Das, R., Spectrum and Fine Spectrum of the Lower Triangular Matrix B(r; o; s) Over the Sequences Spaces, Appl. Math. Inf. Sci, 9, 4(2015), 2139-2145.
  • Zettl, A., Sturm-Liouville Theory, First ed., Amer. Math. Survey and Monographs vol. 121, USA, 2005.

Yıl 2018, Cilt: 10, 173 - 177, 29.12.2018

Rukiye Öztürk Mert Pembe İpek Al Zameddin I. Ismailov

Öz

Kaynakça

  • Akhmedov, A. M., El-Shabrawy, S. R., On the Spectrum of the Generalized Lower Triangle Double-Band Matrices , Lviv, (2010), 17-21.
  • Akhmedov, A. M., El-Shabrawy, S. R., Notes on the Spectrum of Lower Triangular Double-Band Matrices , Thai Journal of Mathematics, 10(2012), 415-421.
  • Baliarsingh, P., Dutta, S., On a Spectral Classi cation of the operator r v Over the Sequence Space c0 , Proc. Math. Acad. Sci. India, Sect. A Phys., 84, 4(2014), 555-561.
  • Başar, F., Karaisa, A., Spectrum and Fine Spectrum of the Generalized Difference Operator De ned by Double Sequential Upper Band Matrix Over the Sequence Spaces lp; (1 < p < 1); Hacet. J. Math., 44, 6(2015), 1315-1332.
  • Böttcher, A., Silbermann, B., Analysis of Teoplitz Operators, Berlin, Springer-Verlag, 1990.
  • Böttcher, A., Grudsky, S., Toeplitz Matrices, Asymptotic Linear Algebra anf Functional Analysis, Berlin, Springer-Verlag, 1991.
  • Dunford, N., Schwartz, J. T., Linear Operators I, II, Second ed., Interscience, New York, 1958; 1963.
  • El-Shabrawy, S. R., Spectra and Fine Spectra of Certain Lower Triangular Double-Band Matrices as Operator on c0 , Journal of Inequalities and Applications, 241, 1(2014), 2-9.
  • Gohberg, I., Goldberg, S., Kaashock, M. A., Basic Classes of Linear Operators, Springer, 1990.
  • Ismailov, Z. I., Otkun Çevik, E., Unluyol, E., Compact Inverses of Multipoint Normal Differential Operators for First Order , Electronic Journal of Differential Equations, 89(2011), 1-11.
  • Jeribi, A., Spectral Theory and Applications of Linear Operators and Block Operator Matrices, Springer, 2015.
  • Karakaya, V., Dzh. Manafov, M., Simsek, N., On the Fine Spectrum of the Second Order Di erence Operator Over the Sequence Spaces lp and bvp; (1 < p < 1) , Mathematical and Computer Modelling, 55(2012), 426-431.
  • Kochubei, A. N., Symmetric Operators and Nonclassical Spectral Problems , Mat. Zametki, 25, 3(1979), 425-434.
  • Langer, M., Strauss, M., Spectral Properties of Unbounded j􀀀Self Adjoint Block Operator Matrices , arXiv:1410.1213 [math.SP], 1-37.
  • Nagel, R. , The Spectrum of Unbounded Operator Matrices with Non-Diagonal Domain, Journal of Functional Analysis , 89(1990), 291-302.
  • Otkun Çevik, E., Ismailov, Z. I., Spectrum of the Direct Sum of Operators, Electronic Journal of Differential Equations , 210(2012), 1-8.
  • Tretter, Ch., Spectral Theory of Block Operator Matrices and Applications, Londan: Imperial CollegePress, 264p, 2008.
  • Tripathy, B. C., Das, R., Spectrum and Fine Spectrum of the Lower Triangular Matrix B(r; o; s) Over the Sequences Spaces, Appl. Math. Inf. Sci, 9, 4(2015), 2139-2145.
  • Zettl, A., Sturm-Liouville Theory, First ed., Amer. Math. Survey and Monographs vol. 121, USA, 2005.
Toplam 19 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Makaleler
Yazarlar

Rukiye Öztürk Mert 0000-0001-8083-5304

Pembe İpek Al

Zameddin I. Ismailov Bu kişi benim

Yayımlanma Tarihi 29 Aralık 2018
Yayımlandığı Sayı Yıl 2018 Cilt: 10

Kaynak Göster

APA Öztürk Mert, R., İpek Al, P., & I. Ismailov, Z. (2018). Characteristic Numbers of Upper Triangular One-Band Block Operator Matrices. Turkish Journal of Mathematics and Computer Science, 10, 173-177.
AMA Öztürk Mert R, İpek Al P, I. Ismailov Z. Characteristic Numbers of Upper Triangular One-Band Block Operator Matrices. TJMCS. Aralık 2018;10:173-177.
Chicago Öztürk Mert, Rukiye, Pembe İpek Al, ve Zameddin I. Ismailov. “Characteristic Numbers of Upper Triangular One-Band Block Operator Matrices”. Turkish Journal of Mathematics and Computer Science 10, Aralık (Aralık 2018): 173-77.
EndNote Öztürk Mert R, İpek Al P, I. Ismailov Z (01 Aralık 2018) Characteristic Numbers of Upper Triangular One-Band Block Operator Matrices. Turkish Journal of Mathematics and Computer Science 10 173–177.
IEEE R. Öztürk Mert, P. İpek Al, ve Z. I. Ismailov, “Characteristic Numbers of Upper Triangular One-Band Block Operator Matrices”, TJMCS, c. 10, ss. 173–177, 2018.
ISNAD Öztürk Mert, Rukiye vd. “Characteristic Numbers of Upper Triangular One-Band Block Operator Matrices”. Turkish Journal of Mathematics and Computer Science 10 (Aralık 2018), 173-177.
JAMA Öztürk Mert R, İpek Al P, I. Ismailov Z. Characteristic Numbers of Upper Triangular One-Band Block Operator Matrices. TJMCS. 2018;10:173–177.
MLA Öztürk Mert, Rukiye vd. “Characteristic Numbers of Upper Triangular One-Band Block Operator Matrices”. Turkish Journal of Mathematics and Computer Science, c. 10, 2018, ss. 173-7.
Vancouver Öztürk Mert R, İpek Al P, I. Ismailov Z. Characteristic Numbers of Upper Triangular One-Band Block Operator Matrices. TJMCS. 2018;10:173-7.
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