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

Lancaster, P; Markus, AS; Psarrakos, P

dc.contributor.author	Lancaster, P	en
dc.contributor.author	Markus, AS	en
dc.contributor.author	Psarrakos, P	en
dc.date.accessioned	2014-03-01T01:18:17Z
dc.date.available	2014-03-01T01:18:17Z
dc.date.issued	2002	en
dc.identifier.issn	0378-620X	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/14923
dc.subject	Eigenvalues	en
dc.subject	Eigenvectors	en
dc.subject	Hilbert Space	en
dc.subject	Numerical Range	en
dc.subject	Satisfiability	en
dc.subject.classification	Mathematics	en
dc.title	Repeated eigenvectors and the numerical range of self-adjoint quadratic operator polynomials	en
heal.type	journalArticle	en
heal.identifier.primary	10.1007/BF01217534	en
heal.identifier.secondary	http://dx.doi.org/10.1007/BF01217534	en
heal.language	English	en
heal.publicationDate	2002	en
heal.abstract	Let L(lambda) 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 partial derivativeW(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 partial derivativeW(L) are semisimple and (in a sense to be defined) they are normal. Also, for any eigenvalue at a point on partial derivativeW(L) where an external cone property is satisfied, the partial multiplicities cannot exceed two.	en
heal.publisher	BIRKHAUSER VERLAG AG	en
heal.journalName	Integral Equations and Operator Theory	en
dc.identifier.doi	10.1007/BF01217534	en
dc.identifier.isi	ISI:000178246800006	en
dc.identifier.volume	44	en
dc.identifier.issue	2	en
dc.identifier.spage	243	en
dc.identifier.epage	253	en