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On Commuting and Semi-commuting Positive Operators (1208.3495v1)
Published 16 Aug 2012 in math.FA
Abstract: Let $K$ be a positive compact operator on a Banach lattice. We prove that if either $[K>$ or $<K]$ is ideal irreducible then $[K>=<K]=L_+(X)\cap {K}'$. 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 Bra\v{c}i\v{c} (2010).
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