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Bounds for the spectral radius of positive operators

✍ Scribed by P. P. Zabreiko; M. A. Krasnosel'skii; V. Ya. Stetsenko

Publisher
SP MAIK Nauka/Interperiodica
Year
1967
Tongue
English
Weight
256 KB
Volume
1
Category
Article
ISSN
0001-4346

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Let K 1 , . . . , K n be (infinite) non-negative matrices that define operators on a Banach sequence space. Given a function f : ) of n variables, we define a nonnegative matrix f (K 1 , . . . , K n ) and consider the inequality where r denotes the spectral radius. We find the largest function f fo

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We develop lower bounds for the spectral radius of symmetric, skew-symmetric, and arbitrary real matrices, Our approach utilizes the well-known Leverrier-Faddeev algorithm for calculating the coefficients of the characteristic polynomial of a matrix in conjunction with a theorem by Lucas which state