Extensions of Perron-Frobenius Theory

2012/08/16 by Niushan Gao, Gao, Niushan
Mathematics · #Advanced Banach Space Theory #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.1208.3490

openalex publication_date 2012/08/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The classical Perron-Frobenius theory asserts that for two matrices A and B, if 0≤ B ≤ 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(μ) 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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