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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On commuting and semi-commuting positive operators


Author: Niushan Gao
Journal: Proc. Amer. Math. Soc. 142 (2014), 2733-2745
MSC (2010): Primary 47B65; Secondary 47A15, 47B47
Published electronically: May 7, 2014
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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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Additional Information

Niushan Gao
Affiliation: Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G2G1
Email: niushan@ualberta.ca

DOI: http://dx.doi.org/10.1090/S0002-9939-2014-12002-8
PII: S 0002-9939(2014)12002-8
Keywords: Ideal irreducible operator, compact positive operator, commuting operators, semi-commuting operators
Received by editor(s): August 14, 2012
Received by editor(s) in revised form: August 31, 2012
Published electronically: May 7, 2014
Communicated by: Thomas Schlumprecht
Article copyright: © Copyright 2014 American Mathematical Society