English

Strong Monotonicity of Spectral Radius of Positive Operators

Functional Analysis 2012-09-11 v2

Abstract

The classic result of Perron and Frobenius states that if AA and BB are matrices with nonnegative elements, such that ABA \leq B, AA is irreducible, and ρ(A)=ρ(B)\rho(A) = \rho(B) then A=BA = B. We extend this result to a large class of band irreducible positive operators on a large class of Banach lattices and provide examples to show that the conditions we put on operators and Banach lattices cannot be weakened.

Keywords

Cite

@article{arxiv.1205.5583,
  title  = {Strong Monotonicity of Spectral Radius of Positive Operators},
  author = {Donald W. Hadwin and Arkady K. Kitover and Mehmet Orhon},
  journal= {arXiv preprint arXiv:1205.5583},
  year   = {2012}
}