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On One Method of Studying Spectral Properties of Non-selfadjoint Operators

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  • Maksim V. Kukushkin

Abstract

In this paper, we explore a certain class of Non-selfadjoint operators acting on a complex separable Hilbert space. We consider a perturbation of a nonselfadjoint operator by an operator that is also nonselfadjoint. Our consideration is based on known spectral properties of the real component of a nonselfadjoint compact operator. Using a technique of the sesquilinear forms theory, we establish the compactness property of the resolvent and obtain the asymptotic equivalence between the real component of the resolvent and the resolvent of the real component for some class of nonselfadjoint operators. We obtain a classification of nonselfadjoint operators in accordance with belonging their resolvent to the Schatten-von Neumann class and formulate a sufficient condition of completeness of the root vector system. Finally, we obtain an asymptotic formula for the eigenvalues.

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  • Maksim V. Kukushkin, 2020. "On One Method of Studying Spectral Properties of Non-selfadjoint Operators," Abstract and Applied Analysis, Hindawi, vol. 2020, pages 1-13, September.
    • Handle: RePEc:hin:jnlaaa:1461647
    DOI: 10.1155/2020/1461647
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    Cited by:

    1. Maria Korovina, 2020. "Asymptotics of Solutions of Linear Differential Equations with Holomorphic Coefficients in the Neighborhood of an Infinitely Distant Point," Mathematics, MDPI, vol. 8(12), pages 1-15, December.
    2. Maksim V. Kukushkin, 2024. "Schatten Index of the Sectorial Operator via the Real Component of Its Inverse," Mathematics, MDPI, vol. 12(4), pages 1-21, February.

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