Spectral properties of unbounded J-self-adjoint block operator matrices

被引：5

作者：

Langer, Matthias ^{[1
]}

Strauss, Michael ^{[2
]}

机构：

[1] Univ Strathclyde, Dept Math & Stat, 26 Richmond St, Glasgow G1 1XH, Lanark, Scotland

[2] Univ Sussex, Dept Math, Falmer Campus, Brighton BN1 9QH, E Sussex, England

来源：

JOURNAL OF SPECTRAL THEORY | 2017年 / 7卷 / 01期

基金：

英国工程与自然科学研究理事会;

关键词：

J-self-adjoint operator; spectral enclosure; Schur complement; quadratic numerical range; Krein space; spectrum of positive type; TRIPLE VARIATIONAL-PRINCIPLES; KREIN SPACES; DEFINITE TYPE; EIGENVALUES;

D O I：

10.4171/JST/158

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the spectrum of unbounded J-self-adjoint block operator matrices. In particular, we prove enclosures for the spectrum, provide a sufficient condition for the spectrumbeing real and derive variational principles for certain real eigenvalues even in the presence of non-real spectrum. The latter lead to lower and upper bounds and asymptotic estimates for eigenvalues.

引用

页码：137 / 190

页数：54

共 36 条

[1] Spectral Estimates and Basis Properties for Self-Adjoint Block Operator Matrices
Michael Strauss
Integral Equations and Operator Theory, 2010, 67 : 257 - 277
[2] Bounds on the Spectrum and Reducing Subspaces of a J-Self-adjoint Operator
Albeverio, Sergio
Motovilov, Alexander K.
Tretter, Christiane
INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2010, 59 (05) : 1737 - 1776
[3] PROPERTIES OF J-SELF-ADJOINT OPERATORS
Jung, Sungeun
OPERATORS AND MATRICES, 2021, 15 (02): : 627 - 644
[4] Spectral Estimates and Basis Properties for Self-Adjoint Block Operator Matrices
Strauss, Michael
INTEGRAL EQUATIONS AND OPERATOR THEORY, 2010, 67 (02) : 257 - 277
[5] Spectral inclusion for unbounded block operator matrices
Tretter, Christiane
JOURNAL OF FUNCTIONAL ANALYSIS, 2009, 256 (11) : 3806 - 3829
[6] Bounds on Variation of Spectral Subspaces under J-Self-adjoint Perturbations
Albeverio, Sergio
Motovilov, Alexander K.
Shkalikov, Andrei A.
INTEGRAL EQUATIONS AND OPERATOR THEORY, 2009, 64 (04) : 455 - 486
[7] On invariant graph subspaces of a J-self-adjoint operator in the Feshbach case
Albeverio, S.
Motovilov, A. K.
MATHEMATICAL NOTES, 2016, 100 (5-6) : 761 - 773
[8] On invariant graph subspaces of a J-self-adjoint operator in the Feshbach case
S. Albeverio
A. K. Motovilov
Mathematical Notes, 2016, 100 : 761 - 773
[9] On J-self-adjoint differential operators similar to self-adjoint operators
Karabash, IM
MATHEMATICAL NOTES, 2000, 68 (5-6) : 798 - 799
[10] Bounds on Variation of Spectral Subspaces under J-Self-adjoint Perturbations
Sergio Albeverio
Alexander K. Motovilov
Andrei A. Shkalikov
Integral Equations and Operator Theory, 2009, 64 : 455 - 486

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