Rukiye Öztürk Mer, Pembe Ipek Al, Zameddin I. İsmailov

Characteristic Numbers of Upper Triangular One-Band Block Operator Matrices

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

PDF

___

[1] Akhmedov, A. M., El-Shabrawy, S. R., On the Spectrum of the Generalized Lower Triangle Double-Band Matrices , Lviv, (2010), 17-21.
[2] 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.
[3] Baliarsingh, P., Dutta, S., On a Spectral Classification of the operator ∆r v Over the Sequence Space c0 , Proc. Math. Acad. Sci. India, Sect. A Phys., 84, 4(2014), 555-561.
[4] Başar, F., Karaisa, A., Spectrum and Fine Spectrum of the Generalized Difference Operator Defined by Double Sequential Upper Band Matrix Over the Sequence Spaces lp, (1 < p < ∞), Hacet. J. Math., 44, 6(2015), 1315-1332.
[5] Bottcher, A., Silbermann, B., Analysis of Teoplitz Operators, Berlin, Springer-Verlag, 1990.
[6] Bottcher, A., Grudsky, S., Toeplitz Matrices, Asymptotic Linear Algebra anf Functional Analysis, Berlin, Springer-Verlag, 1991.
[7] Dunford, N., Schwartz, J. T., Linear Operators I, II, Second ed., Interscience, New York, 1958; 1963.
[8] 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.
[9] Gohberg, I., Goldberg, S., Kaashock, M. A., Basic Classes of Linear Operators, Springer, 1990.
[10] 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.
[11] Jeribi, A., Spectral Theory and Applications of Linear Operators and Block Operator Matrices, Springer, 2015.
[12] Karakaya, V., Dzh. Manafov, M., S¸ims¸ek, N., On the Fine Spectrum of the Second Order Difference Operator Over the Sequence Spaces lp and bvp, (1 < p < ∞) , Mathematical and Computer Modelling, 55(2012), 426-431.
[13] Kochubei, A. N., Symmetric Operators and Nonclassical Spectral Problems , Mat. Zametki, 25, 3(1979), 425-434.
[14] Langer, M., Strauss, M., Spectral Properties of Unbounded j−Self Adjoint Block Operator Matrices , arXiv:1410.1213 [math.SP], 1-37.
[15] Nagel, R. , The Spectrum of Unbounded Operator Matrices with Non-Diagonal Domain, Journal of Functional Analysis , 89(1990), 291-302.
[16] Otkun C¸ evik, E., Ismailov, Z. I., Spectrum of the Direct Sum of Operators, Electronic Journal of Differential Equations , 210(2012), 1-8.
[17] Tretter, Ch., Spectral Theory of Block Operator Matrices and Applications, Londan: Imperial CollegePress, 264p, 2008.
[18] 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.
[19] Zettl, A., Sturm-Liouville Theory, First ed., Amer. Math. Survey and Monographs vol. 121, USA, 2005.