Spectrum localization of a perturbed operator in a strip and applications

• Autorzy: Gil Michael

Identyfikatory

DOI

10.7494/OpMath.2021.41.3.395

• Języki publikacji: EN

Abstrakty

EN

Let A and A be bounded operators in a Hilbert space. We consider the following problem: let the spectrum of A lie in some strip. In what strip the spectrum of A lies if A and Ä are “close”? Applications of the obtained results to integral operators and matrices are also discussed. In addition, we apply our perturbation results to approximate the spectral strip of a Hilbert-Schmidt operator by the spectral strips of finite matrices.

Słowa kluczowe

EN

operator; spectrum; perturbation; approximation; integral operator; matrix

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2021
• Tom: Vol. 41, no. 3
• Strony: 395–--412
• Opis fizyczny: Bibliogr. 24 poz.

Twórcy

autor

Gil Michael

• Department of Mathematics Ben Gurion University of the Negev P.0. Box 653, Beer-Sheva 84105, Israel

• https://orcid.org/0000-0002-6404-9618

Bibliografia

• [1] B. Abdelmoumen, A. Jeribi, M. Mnif, Invariance of the Schechter essential spectrum under polynomial ly compact operator perturbation, Extracta Math. 26 (2011), no. 1, 61-73.
• [2] P. Aiena, S. Triolo, Some perturbation results through localized SVEP, Acta Sci. Math. (Szeged) 82 (2016), no. 1-2, 205-219.
• [3] P. Aiena, S. Triolo, Weyl-type theorems on Banach spaces under compact perturbations, Mediterr. J. Math. 15 (2018), no. 3, Paper no. 126, 18 pp.
• [4] A.D. Baranov, D.V. Yakubovich, Completeness of rank one perturbations of normal operators with lacunary spectrum, J. Spectr. Theory 8 (2018), no. 1, 1-32.
• [5] S. Buterin, S.V. Vasiliev, On uniqueness of recovering the convolution integro-differential operator from the spectrum of its non-smooth one-dimensional perturbation, Bound. Value Probl. (2018), Paper no. 55, 12 pp.
• [6] W. Chaker, A. Jeribi, B. Krichen, Demicompact linear operators, essential spectrum and some perturbation results, Math. Nachr. 288 (2015), no. 13, 1476-1486.
• [7] X. Claeys, Essential spectrum of local multi-trace boundary integral operators, IMA J. Appl. Math. 81 (2016), no. 6, 961-983.
• [8] Yu.L. Daleckii, M.G. Krein, Stability of Solutions of Differential Equations in Banach Space, Amer. Math. Soc., Providence, R.I., 1974.
• [9] E. Fedele, A. Pushnitski, Weighted integral Hankel operators with continuous spectrum, Concr. Oper. 4 (2017), no. 1, 121-129.
• [10] M.I. Gil’, Invertibility conditions and bounds for spectra of matrix integral operators, Monatsh. Math. 129 (2000), 15-24.
• [11] M.I. Gil’, Spectrum perturbations of operators on tensor products of Hilbert spaces, J. Math. Kyoto Univ. 43 (2004), no. 4, 719-735.
• [12] M.I. Gil’, Spectrum and resolvent of a partial integral operator, Appl. Anal. 87 (2008), no. 5, 555-566.
• [13] M.I. Gil’, Spectral approximations of unbounded non-selfadjoint operators, Analysis and Mathem. Physics 3 (2013), no. 1, 37-44.
• [14] M.I. Gil’, Spectral approximations of unbounded operators of the type “normal plus compact”, Funct. et Approx. Comment. Math. 51 (2014), no. 1, 133-140.
• [15] M.I. Gil’, Operator Functions and Operator Equations, World Scientific, New Jersey, 2018.
• [16] M.I. Gil’, Norm estimates for resolvents of linear operators in a Banach space and spectral variations, Adv. Oper. Theory 4 (2019), no. 1, 113-139.
• [17] T. Kato, Perturbation Theory for Linear Operators, Springer-Verlag, Berlin, 1980.
• [18] R. Killip, Perturbations of one-dimensional Schrödinger operators preserving the absolutely continuous spectrum, Int. Math. Res. Not. 38 (2002), 2029-2061.
• [19] M. Malejki, Approximation of eigenvalues of some unbounded self-adjoint discrete Jacobi matrices by eigenvalues of finite submatrices, Opuscula Math. 27 (2007), no. 1, 37-49.
• [20] M. Malejki, Approximation and asymptotics of eigenvalues of unbounded self-adjoint Jacobi matrices acting in l2 by the use of finite submatrices, Cent. Eur. J. Math. 8 (2010), no. 1, 114-128.
• [21] G.V. Milovanovic, D.S. Mitrinovic, Th.M. Rassias, Topics in Polynomials: Extremal Problems, Inequalities, Zeros, World Scientific Publishing Co., Inc., River Edge, NJ, 1994.
• [22] P.M. Pardalos, Th.M. Rassias (eds.), Contributions in Mathematics and Engineering, Springer International Publishing, Switzerland, 2016.
• [23] Th.M. Rassias, V.A. Zagrebnov (eds.), Analysis and Operator Theory. Dedicated in Memory of Tosio Kato’s 100th Birthday, Springer, NY, 2019.
• [24] M.L. Sahari, A.K. Taha, L. Randriamihamison, A note on the spectrum of diagonal perturbation of weighted shift operator, Matematiche (Catania) 74 (2019), no. 1, 35-47.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).