Spectral estimates and basis properties for self-adjoint block operator matrices

Michael Strauss

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

In the first part of this manuscript a relationship between the spectrum of self-adjoint operator matrices and the spectra of their diagonal entries is found. This leads to enclosures for spectral points and in particular, enclosures for eigenvalues. We also consider graph invariant subspaces, and their corresponding angular operators. The existence of a bounded angular operator leads to basis properties of the first component of eigenvectors of operator matrices for which the corresponding eigenvalues lie in a half line. The results are applied to an example from magnetohydrodynamics.
LanguageEnglish
Pages257-277
Number of pages21
JournalIntegral Equations and Operator Theory
Volume67
Issue number2
DOIs
Publication statusPublished - 2010

Fingerprint

Operator Matrix
Block Matrix
Enclosure
Eigenvalue
Graph Invariants
Invariant Subspace
Operator
Self-adjoint Operator
Estimate
Eigenvector
Half line
Relationships

Keywords

  • schur complement
  • magnetohydrodynamics
  • bari basis
  • angular operator
  • graph invariant subspace
  • eigenvalue estimates

Cite this

@article{44e2d68763c243baaef050f8a3b43f28,
title = "Spectral estimates and basis properties for self-adjoint block operator matrices",
abstract = "In the first part of this manuscript a relationship between the spectrum of self-adjoint operator matrices and the spectra of their diagonal entries is found. This leads to enclosures for spectral points and in particular, enclosures for eigenvalues. We also consider graph invariant subspaces, and their corresponding angular operators. The existence of a bounded angular operator leads to basis properties of the first component of eigenvectors of operator matrices for which the corresponding eigenvalues lie in a half line. The results are applied to an example from magnetohydrodynamics.",
keywords = "schur complement, magnetohydrodynamics, bari basis, angular operator, graph invariant subspace , eigenvalue estimates",
author = "Michael Strauss",
year = "2010",
doi = "10.1007/s00020-010-1780-0",
language = "English",
volume = "67",
pages = "257--277",
journal = "Integral Equations and Operator Theory",
issn = "0378-620X",
number = "2",

}

Spectral estimates and basis properties for self-adjoint block operator matrices. / Strauss, Michael.

In: Integral Equations and Operator Theory, Vol. 67, No. 2, 2010, p. 257-277.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Spectral estimates and basis properties for self-adjoint block operator matrices

AU - Strauss, Michael

PY - 2010

Y1 - 2010

N2 - In the first part of this manuscript a relationship between the spectrum of self-adjoint operator matrices and the spectra of their diagonal entries is found. This leads to enclosures for spectral points and in particular, enclosures for eigenvalues. We also consider graph invariant subspaces, and their corresponding angular operators. The existence of a bounded angular operator leads to basis properties of the first component of eigenvectors of operator matrices for which the corresponding eigenvalues lie in a half line. The results are applied to an example from magnetohydrodynamics.

AB - In the first part of this manuscript a relationship between the spectrum of self-adjoint operator matrices and the spectra of their diagonal entries is found. This leads to enclosures for spectral points and in particular, enclosures for eigenvalues. We also consider graph invariant subspaces, and their corresponding angular operators. The existence of a bounded angular operator leads to basis properties of the first component of eigenvectors of operator matrices for which the corresponding eigenvalues lie in a half line. The results are applied to an example from magnetohydrodynamics.

KW - schur complement

KW - magnetohydrodynamics

KW - bari basis

KW - angular operator

KW - graph invariant subspace

KW - eigenvalue estimates

UR - http://www.springerlink.com/content/1715745100168513/

U2 - 10.1007/s00020-010-1780-0

DO - 10.1007/s00020-010-1780-0

M3 - Article

VL - 67

SP - 257

EP - 277

JO - Integral Equations and Operator Theory

T2 - Integral Equations and Operator Theory

JF - Integral Equations and Operator Theory

SN - 0378-620X

IS - 2

ER -