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 and are matrices with nonnegative elements, such that , is irreducible, and then . 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}
}