Strong Monotonicity of Spectral Radius of Positive Operators

2012/05/24 by Donald W. Hadwin, Hadwin, Donald W., Arkady Kitover +3
Mathematics · #46B42 #47B65 #Advanced Banach Space Theory #Advanced Operator Algebra Research #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.1205.5583

openalex publication_date 2012/05/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The classic result of Perron and Frobenius states that if A and B are matrices with nonnegative elements, such that A ≤ B, A is irreducible, and ρ(A) = ρ(B) then A = B. We extend this result to a large class of band irreducible positive operators on a large class of Banach lattices and provide examples to show that the conditions we put on operators and Banach lattices cannot be weakened.

Citations

• Extensions of Perron-Frobenius Theory

Related

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• Irreducible Semigroups of Positive Operators on Banach Lattices
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