Geodesic
On some formulas for the index of linear bounded operator
Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 3 (2009), pp. 3-9 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider the linear bounded operator in infinite dimensional separable Hilbert space satisfying some conditions. We prove formulas that can be used to calculate the index of this operator.
Keywords: operator, index, trace, absolute norm. 
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I. G. Khachatryan. On some formulas for the index of linear bounded operator. Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 3 (2009), pp. 3-9. http://geodesic.mathdoc.fr/item/UZERU_2009_3_a0/

[1] B.V. Fedosov, “Index Theorems. Partial Differential Equations”, Itogi Nauki i Tekhniki, 8, Akad. Nauk SSSR, Vsesoyuz. Inst. Nauchn. i Tekhn. Inform., M, 1991, 165–275 (in Russian) | MR

[2] N.I. Akhiezer, I.M. Glazman, Theory of Linear Operators in Hilbert Space, Nauka, M, 1966 (in Russian)

[3] I.C. Gohberg, M.G. Krein, Introduction to the Theory of Linear Nonself-Adjoint Operators, Nauka, M, 1965 (in Russian) | MR

[4] V.B. Lidskii, “Nonselfadjoint Operators with a Trace”, DAN SSSR, 125:3 (1959), 485–488 (in Russian) | MR

[5] L.A. Lusternik, V.J. Sobolev, Elements of Functional Analysis., Nauka, M, 1965 (in Russian) | MR

[6] I.G. Khachatryan, “On the Inversibility of some Furier Type Integral Operators”, Uchenie Zapiski EGU (Proceedings of the YSU), 2004, no. 2, 3–6 (in Russian)

[7] I.G. Khachatryan, “On a Trace Formula”, Izvestia AN Arm. SSR, Matematika, 20:1 (1985), 41–52 (in Russian) | MR | Zbl

[8] V.A. Marchenko, Sturm-Liouville Operators and Applications., Naukova Dumka, Kiev, 1977 (in Russian) | MR | Zbl

[9] Z.S. Agranovich, V.A. Marchenko, The Inverse Problem of the Scattering Theory., Kharkov, 1960 (in Russian)