On angular localization of spectra of perturbed operators

Autores/as

  • M.I. Gil' Department of Mathematics, Ben Gurion University of the Negev P.O. Box 653, Beer-Sheva 84105, Israel

DOI:

https://doi.org/10.17398/2605-5686.35.2.197

Palabras clave:

Operators, spectrum, angular location, perturbations, integral operator

Resumen

Let A and à be bounded operators in a Hilbert space. We consider the following problem: let the spectrum of A lie in some angular sector. In what sector the spectrum of à lies if A and à are “close”? Applications of the obtained results to integral operators are also discussed.

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Referencias

Yu.L. Daleckii, M.G. Krein, “Stability of Solutions of Differential Equations in Banach Space”, Vol. 43, American Mathematical Society, Providence, R. I., 1974.

M.I. Gil’, “Operator Functions and Operator Equations”, World Scientific Publishing Co. Pte. Ltd., Hackensack, New Jersey, 2018.

M.I. Gil’, Norm estimates for resolvents of linear operators in a Banach space and spectral variations, Adv. Oper. Theory 4 (1) (2019), 113 – 139.

G.H. Hostetter, An improved test for the zeros of a polynomial in a sector, IEEE Trans. Automatic Control AC-20 (3) (1975), 433 – 434.

E.I. Jury, N.K. Bose, B.D.O. Anderson, A simple test for zeros of a complex polynomial in a sector, IEEE Trans. Automatic Control AC-19 (1974), 437 – 438.

E.I. Jury, N.K. Bose, B.D.O. Anderson, On eigenvalues of complex matrices in a sector, IEEE Trans. Automatic Control AC-20 (1975), 433 – 434.

M.G. Krein, The angular localization of the spectrum of a multiplicative integral in Hilbert space (in Russian) Funkcional. Anal. i Prilozhen 3 (1) (1969), 89 – 90.

G.V. Rozenblyum, Angular asymptotics of the spectrum of operators that are close to normal, J. Soviet Math. 45 (3) (1989), 1250 – 1261.

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Publicado

2020-12-01

Número

Sección

Banach Spaces and Operator Theory

Cómo citar

On angular localization of spectra of perturbed operators. (2020). Extracta Mathematicae, 35(2), 197-204. https://doi.org/10.17398/2605-5686.35.2.197