Variations of real and imaginary parts of eigenvalues of compact operators under perturbations

Michael Gil’

doi:10.1007/s13324-023-00826-6

Variations of real and imaginary parts of eigenvalues of compact operators under perturbations

Michael Gil’

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

Let A and S be compact operators in a Hilbert space, and S be selfadjoint. Under certain conditions we derive bounds for the quantities supkinfj|Reλk(A)-λj(S)| and supkinfj|Imλk(A)-λj(S)| , where λ_k(A) (k= 1 , 2 ,..) are the eigenvalues of A. We also discuss applications of the obtained bounds to the theory of Jacobi and Schatten–von Neumann operators.

Original language	English
Article number	61
Journal	Analysis and Mathematical Physics
Volume	13
Issue number	4
DOIs	https://doi.org/10.1007/s13324-023-00826-6
State	Published - 1 Aug 2023

Keywords

Compact operators
Hilbert space
Jacobi operator
Perturbations
Schatten–von Neumann operator

ASJC Scopus subject areas

Analysis
Algebra and Number Theory
Mathematical Physics

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10.1007/s13324-023-00826-6

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abstract = "Let A and S be compact operators in a Hilbert space, and S be selfadjoint. Under certain conditions we derive bounds for the quantities supkinfj|Reλk(A)-λj(S)| and supkinfj|Imλk(A)-λj(S)| , where λk(A) (k= 1 , 2 ,..) are the eigenvalues of A. We also discuss applications of the obtained bounds to the theory of Jacobi and Schatten–von Neumann operators.",

keywords = "Compact operators, Hilbert space, Jacobi operator, Perturbations, Schatten–von Neumann operator",

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N2 - Let A and S be compact operators in a Hilbert space, and S be selfadjoint. Under certain conditions we derive bounds for the quantities supkinfj|Reλk(A)-λj(S)| and supkinfj|Imλk(A)-λj(S)| , where λk(A) (k= 1 , 2 ,..) are the eigenvalues of A. We also discuss applications of the obtained bounds to the theory of Jacobi and Schatten–von Neumann operators.

AB - Let A and S be compact operators in a Hilbert space, and S be selfadjoint. Under certain conditions we derive bounds for the quantities supkinfj|Reλk(A)-λj(S)| and supkinfj|Imλk(A)-λj(S)| , where λk(A) (k= 1 , 2 ,..) are the eigenvalues of A. We also discuss applications of the obtained bounds to the theory of Jacobi and Schatten–von Neumann operators.

KW - Compact operators

KW - Hilbert space

KW - Jacobi operator

KW - Perturbations

KW - Schatten–von Neumann operator

UR - https://www.scopus.com/pages/publications/85163725281

U2 - 10.1007/s13324-023-00826-6

DO - 10.1007/s13324-023-00826-6

M3 - Article

AN - SCOPUS:85163725281

SN - 1664-2368

VL - 13

JO - Analysis and Mathematical Physics

JF - Analysis and Mathematical Physics

IS - 4

M1 - 61

ER -

Variations of real and imaginary parts of eigenvalues of compact operators under perturbations

Abstract

Keywords

ASJC Scopus subject areas

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