Characteristic Numbers of Upper Triangular One-Band Block Operator Matrices

Year 2018, Volume: 10, 173 - 177, 29.12.2018

Rukiye Öztürk Mert , Pembe İpek Al , Zameddin I. Ismailov

Abstract

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.

Keywords

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

References

• 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 Dierence 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.