Factorization of selfadjoint operator polynomials

P. Lancaster, A. Markus, V. Matsaev

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


Factorization theorems ate obtained for selfadjoint operator poly-nomials L(λ):= εn j=0 λj Aj where A0, A1,..., An are selfadjoint bounded linear operators on a Hilbert space H{small}. The essential hypotheses concern the real spectrum of L(λ) and, in particular, ensure the existence of spectral sub-spaces associated with the real line for the (companion) linearization. Under suitable additional conditions, the main results assert the existence of polynomial factors (a) of degrees [1/2n] and [1/2(n + 1)] when the leading coefficient An is strictly positive and (b) of degree 1/2n (when n is even) when An is in-vertible and the spectrum of L (λ) is real. Consequences for the factorization of regular operator polynomials (when L(α) is invertible for some real α) are also discussed.

Original languageEnglish
Pages (from-to)337-348
Number of pages12
JournalJournal of Operator Theory
Issue number2
StatePublished - 1 Dec 1996


  • Companion operator
  • Selfadjoint operator polynomial
  • Spectral factorisation
  • Supporting subspace

ASJC Scopus subject areas

  • Algebra and Number Theory


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