On Spectral Properties of some Class of Non-selfadjoint Operators
Abstract
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.
Keywords
Cite
@article{arxiv.1807.00047,
title = {On Spectral Properties of some Class of Non-selfadjoint Operators},
author = {M. V. Kukushkin},
journal= {arXiv preprint arXiv:1807.00047},
year = {2019}
}
Comments
The report devoted to the results of this work took place 06.12.2017 at the seminar of the Department of mathematical physics St. Petersburg state University, Saint Petersburg branch of V.A.Steklov Mathematical Institute of the Russian Academy of science, Russia, Saint Petersburg. arXiv admin note: text overlap with arXiv:1804.10840