TY - JOUR
T1 - Spectrum of definite type of self-adjoint operators in Krein spaces
AU - Langer, Heinz
AU - Langer, Matthias
AU - Markus, Alexander
AU - Tretter, Christiane
N1 - Funding Information:
The authors gratefully acknowledge the support of the British Engineering and Physical Sciences Research Council, EPSRC, under Grant No. GR/R40753 and of the Research Training Network HPRN-CT-2000-00116 of the European Union. The second author also acknowledges the support of the ‘Fonds zur Förderung der wissenschaftlichen Forschung’ of Austria, FWF, Grant No. P 15540–N 05.
PY - 2005/3/1
Y1 - 2005/3/1
N2 - For a self-adjoint operator in a Krein space we construct an interval [ν, μ] outside of which the operator has only a spectrum of definite type and possesses a local spectral function. As a consequence, a spectral subspace corresponding to an interval outside [ν, μ] admits an angular operator representation. We describe a defect subspace of the domain of the angular operator in terms of the Schur complement, and we derive variational principles for the discrete eigenvalues in such intervals of definite type.
AB - For a self-adjoint operator in a Krein space we construct an interval [ν, μ] outside of which the operator has only a spectrum of definite type and possesses a local spectral function. As a consequence, a spectral subspace corresponding to an interval outside [ν, μ] admits an angular operator representation. We describe a defect subspace of the domain of the angular operator in terms of the Schur complement, and we derive variational principles for the discrete eigenvalues in such intervals of definite type.
KW - Krein space
KW - Local spectral function
KW - Quadratic numerical range
KW - Spectrum of definite type
KW - Variational principle for eigenvalues
UR - http://www.scopus.com/inward/record.url?scp=17744391427&partnerID=8YFLogxK
U2 - 10.1080/03081080500055049
DO - 10.1080/03081080500055049
M3 - Article
AN - SCOPUS:17744391427
SN - 0308-1087
VL - 53
SP - 115
EP - 136
JO - Linear and Multilinear Algebra
JF - Linear and Multilinear Algebra
IS - 2
ER -