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

Marek, Ivo. "On the polynomial eigenvalue problem with positive operators and location of the spectral radius." Aplikace matematiky 14.2 (1969): 146-159. <http://eudml.org/doc/14586>.

@article{Marek1969,
abstract = {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.},
author = {Marek, Ivo},
journal = {Aplikace matematiky},
keywords = {functional analysis},
language = {eng},
number = {2},
pages = {146-159},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the polynomial eigenvalue problem with positive operators and location of the spectral radius},
url = {http://eudml.org/doc/14586},
volume = {14},
year = {1969},
}

TY - JOUR
AU - Marek, Ivo
TI - On the polynomial eigenvalue problem with positive operators and location of the spectral radius
JO - Aplikace matematiky
PY - 1969
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 14
IS - 2
SP - 146
EP - 159
AB - 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.
LA - eng
KW - functional analysis
UR - http://eudml.org/doc/14586
ER -