TY - JOUR
T1 - Repeated eigenvectors and the numerical range of self-adjoint quadratic operator polynomials
AU - Lancaster, Peter
AU - Markus, Alexander S.
AU - Psarrakos, Panayiotis
PY - 2002/12/3
Y1 - 2002/12/3
N2 - Let L(λ) be a self-adjoint quadratic operator polynomial on a Hilbert space with numerical range W(L). The main concern of this paper is with properties of eigenvalues on ∂W(L). The investigation requires a careful discussion of repeated eigenvectors of more general operator polynomials. It is shown that, in the self-adjoint quadratic case, non-real eigenvalues on ∂W(L) are semisimple and (in a sense to be defined) they are normal. Also, for any eigenvalue at a point on ∂W(L) where an external cone property is satisfied, the partial multiplicities cannot exceed two.
AB - Let L(λ) be a self-adjoint quadratic operator polynomial on a Hilbert space with numerical range W(L). The main concern of this paper is with properties of eigenvalues on ∂W(L). The investigation requires a careful discussion of repeated eigenvectors of more general operator polynomials. It is shown that, in the self-adjoint quadratic case, non-real eigenvalues on ∂W(L) are semisimple and (in a sense to be defined) they are normal. Also, for any eigenvalue at a point on ∂W(L) where an external cone property is satisfied, the partial multiplicities cannot exceed two.
UR - http://www.scopus.com/inward/record.url?scp=0036436087&partnerID=8YFLogxK
U2 - 10.1007/BF01217534
DO - 10.1007/BF01217534
M3 - Article
AN - SCOPUS:0036436087
SN - 0378-620X
VL - 44
SP - 243
EP - 253
JO - Integral Equations and Operator Theory
JF - Integral Equations and Operator Theory
IS - 2
ER -