Some properties of the spectral radius of a monic operator polynomial with nonnegative compact coefficients

Förster, K.-H.; Nagy, B.

doi:10.1007/bf01198938

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Cited by 8 publications

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“…An extension of Perron-Frobenius theory to positive operators on Banach lattices is pursued in [29]. The peripheral spectrum of the monic polynomial in (1.1) when the coefficients are positive (compact) operators in a Banach lattice are considered in [7,18,27]. In addition, the spectral properties of Perron polynomials are examined in [8,9] via a partial linearization based on expansion graphs that were introduced in [10].…”

Section: Introductionmentioning

confidence: 99%

A primer of Perron–Frobenius theory for matrix polynomials

Psarrakos

Tsatsomeros

2004

Linear Algebra and its Applications

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We present an extension of Perron-Frobenius theory to the spectra and numerical ranges of Perron polynomials, namely, matrix polynomials of the formwhere the coefficient matrices are entrywise nonnegative. Our approach relies on the companion matrix linearization. First, we recount the generalization of the Perron-Frobenius Theorem to Perron polynomials and report some of its consequences. Subsequently, we examine the role of L(λ) in multistep difference equations and provide a multistep version of the Fundamental Theorem of Demography. Finally, we extend Issos' results on the numerical range of nonnegative matrices to Perron polynomials.

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