Displaying similar documents to “On 𝒦 -positive elements of the spectral resolution of a 𝒦 -positive operator”

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

Ivo Marek (1969)

Aplikace matematiky

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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.