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

被引:0
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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;
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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.
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页码:284 / 298
页数:14
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