Spectrum separation and inertia for operator polynomials (Q1206895)

The concept of Bezoutian of operator polynomials [see the authors and \textit{M. Tismenetsky}, J. Math. Anal. Appl. 103, 83-102 (1984; Zbl 0567.47016)] is used to generalize to operator polynomials in Hilbert space some results proved for matrix polynomials by the first author and \textit{M. Tismenetsky} [Integral Equations Oper, Theory 5, 386-445 (1982; Zbl 0504.47020)]. Results proved here are applied to linear homogeneous differential equations whose coefficients are constant linear operators in Hilbert space and to orthogonal operator polynomials.