Repeated eigenvectors and the numerical range of self-adjoint quadratic operator polynomials

Peter Lancaster, Alexander S. Markus, Panayiotis Psarrakos

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

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.

Original languageEnglish
Pages (from-to)243-253
Number of pages11
JournalIntegral Equations and Operator Theory
Volume44
Issue number2
DOIs
StatePublished - 3 Dec 2002

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