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- W2022161806 abstract "The classical Perron–Frobenius theory asserts that, for two matrices $$A$$ and $$B$$ , if $$0le B le A$$ and $$r(A)=r(B)$$ with $$A$$ being irreducible, then $$A=B$$ . It has been extended to infinite-dimensional Banach lattices under certain additional conditions, including that $$r(A)$$ is a pole of the resolvent of $$A$$ . In this paper, we prove that the same result holds if $$B$$ is irreducible and $$r(B)$$ is a pole of the resolvent for $$B$$ . We also prove some other interesting extensions of the theorem for infinite-dimensional Banach lattices." @default.
- W2022161806 created "2016-06-24" @default.
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- W2022161806 date "2012-11-28" @default.
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- W2022161806 title "Extensions of Perron–Frobenius theory" @default.
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- W2022161806 doi "https://doi.org/10.1007/s11117-012-0215-3" @default.
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