English

On Commuting and Semi-commuting Positive Operators

Functional Analysis 2012-08-20 v1

Abstract

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

Keywords

Cite

@article{arxiv.1208.3495,
  title  = {On Commuting and Semi-commuting Positive Operators},
  author = {Niushan Gao},
  journal= {arXiv preprint arXiv:1208.3495},
  year   = {2012}
}
R2 v1 2026-06-21T21:51:47.628Z