Geodesic
On the polynomial eigenvalue problem with positive operators and location of the spectral radius
Applications of Mathematics, Tome 14 (1969) no. 2, pp. 146-159.

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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 $F$, $F(\lambda)=\lambda^mA_0-\sum^m_{k=1} \lambda^{m-k}A_k$ with the maximal absolute value. It is assumed that $A_1,\ldots,A_m,A^{-1}_0$ are bounded linear operators mapping a Banach space into itself. Further, it is assumed that the operators $B_j$, where $B_j=A^{-1}_0 A_j, j=1,2,\ldots,m$, leave a cone invariant.
DOI : 10.21136/AM.1969.103217
Classification : 47-30
Keywords: functional analysis 
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Marek, Ivo. On the polynomial eigenvalue problem with positive operators and location of the spectral radius. Applications of Mathematics, Tome 14 (1969) no. 2, pp. 146-159. doi : 10.21136/AM.1969.103217. http://geodesic.mathdoc.fr/articles/10.21136/AM.1969.103217/

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