On the basis property of root vectors of a perturbed self-adjoint operator

被引：0

作者：

A. A. Shkalikov

机构：

[1] Moscow State University,Faculty of Mechanics and Mathematics

来源：

Proceedings of the Steklov Institute of Mathematics | 2010年 / 269卷

关键词：

STEKLOV Institute; Dirac Operator; Selfadjoint Operator; Riesz Basis; Unconditional Basis;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

We study perturbations of a self-adjoint operator T with discrete spectrum such that the number of its points on any unit-length interval of the real axis is uniformly bounded. We prove that if ‖Bϕn‖ ≤ const, where ϕn is an orthonormal system of eigenvectors of the operator T, then the system of root vectors of the perturbed operator T + B forms a basis with parentheses. We also prove that the eigenvalue-counting functions of T and T + B satisfy the relation |n(r, T) − n(r, T + B)| ≤ const.

引用

页码：284 / 298

页数：14

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