On Commuting and Semi-commuting Positive Operators

2012/08/16 by Niushan Gao, Gao, Niushan · 1 citation
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #math.FA

paper · pdf · doi:10.48550/arxiv.1208.3495

arxiv created 2012/08/16 · arxiv updated 2012/08/20

Abstract

Let K be a positive compact operator on a Banach lattice. We prove that if either [K> or <K] is ideal irreducible then [K>=<K]=L₊(X)∩ K'. We also establish the Perron-Frobenius Theorem for such operators K. Finally we apply the results to answer questions in Abramovich and Aliprantis (2002) and Bračič (2010).

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