On commuting and semi-commuting positive operators

Gao, Niushan

doi:10.1090/S0002-9939-2014-12002-8

On commuting and semi-commuting positive operators
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Proc. Amer. Math. Soc. 142 (2014), 2733-2745 Request permission

Abstract:

Let $K$ be a positive compact operator on a Banach lattice. We prove that if either $[K\rangle$ or $\langle K]$ is ideal irreducible, then $[K\rangle =\langle K]=L_+(X)\cap \{K\}’$. We also establish the Perron-Frobenius Theorem for such operators $K$. Finally, we apply our results to answer questions posed by Abramovich and Aliprantis (2002) and Bračič et al. (2010).

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