English

Extensions of Perron-Frobenius Theory

Functional Analysis 2012-08-20 v1

Abstract

The classical Perron-Frobenius theory asserts that for two matrices AA and BB, if 0BA0\leq B \leq A and r(A)=r(B)r(A)=r(B) with AA being irreducible, then A=BA=B. This was recently extended in Bernik et al. (2012) to positive operators on Lp(μ)L_p(\mu) with either AA or BB being irreducible and power compact. In this paper, we extend the results to irreducible operators on arbitrary Banach lattices.

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Cite

@article{arxiv.1208.3490,
  title  = {Extensions of Perron-Frobenius Theory},
  author = {Niushan Gao},
  journal= {arXiv preprint arXiv:1208.3490},
  year   = {2012}
}