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On the polynomial eigenvalue problem with positive operators and location of the spectral radius

Ivo Marek — 1969

Aplikace matematiky

The purpose of this article is to give some estimates for the spectral radius of the polynomial eigenvalue problem, i.e. to derive some estimates for the singularity of the operator-function F , F ( λ ) = λ m A 0 - k = 1 m λ m - k A k with the maximal absolute value. It is assumed that A 1 , ... , A m , A 0 - 1 are bounded linear operators mapping a Banach space into itself. Further, it is assumed that the operators B j , where B j = A 0 - 1 A j , j = 1 , 2 , ... , m , leave a cone invariant.

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