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arXiv · 1208.3490

Extensions of Perron-Frobenius Theory

Niushan Gao
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Abstract

The classical Perron-Frobenius theory asserts that for two matrices $A$ and $B$, if $0\leq B \leq A$ and $r(A)=r(B)$ with $A$ being irreducible, then $A=B$. This was recently extended in Bernik et al. (2012) to positive operators on $L_p(\mu)$ with either $A$ or $B$ being irreducible and power compact. In this paper, we extend the results to irreducible operators on arbitrary Banach lattices.

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Niushan Gao. 2012-08-16. Extensions of Perron-Frobenius Theory. https://arxiv.org/abs/1208.3490

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