2018/06/29 by Maksim V. Kukushkin, Kukushkin, M. V.
Mathematics · #47A07 #47A10 #47B10 #47B25 #Differential Equations and Boundary Problems #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.1807.00047
openalex publication_date 2018/06/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we explore a certain class of non-selfadjoint operators acting in a complex separable Hilbert space. We consider a perturbation of a non-selfadjoint operator by an operator that is also non-selfadjoint. Our consideration is based on known spectral properties of the real component of a non-selfadjoint compact operator. Using a technic of the sesquilinear form theory we establish the compactness property of the resolvent, obtain the asymptotic equivalence between the real component of the resolvent and the resolvent of the real component for some class of non-selfadjoint operators. We obtain a classification of non-selfadjoint operators in accordance with belonging their resolvent to the Schatten-von Neumann class and formulate a sufficient condition of completeness of the root vectors system. Finally we obtain an asymptotic formula for eigenvalues of the considered class of non-selfadjoint operators.