A note on lattice ordered C∗-algebras and Perron-Frobenius theory

A Note on the Proof of the Perron-Frobenius Theorem

This paper provides a simple proof for the Perron-Frobenius theorem concerned with positive matrices using a homotopy technique. By analyzing the behaviour of the eigenvalues of a family of positive matrices, we observe that the conclusions of Perron-Frobenius theorem will hold if it holds for the starting matrix of this family. Based on our observations, we develop a simple numerical technique...

Perron-frobenius Theory for Complex Matrices

The purpose of this paper is to present a unified Perron-Frobenius Theory for nonnegative, for real not necessarily nonnegative and for general complex matrices. The sign-real spectral radius was introduced for general real matrices. This quantity was shown to share certain properties with the Perron root of nonnegative matrices. In this paper we introduce the sign-complex spectral radius. Agai...

Perron-frobenius Theory for Positive Maps on Trace Ideals

This article provides sufficient conditions for positive maps on the Schatten classes Jp; 1 p < 1 of bounded operators on a separable Hilbert space such that a corresponding Perron-Frobenius theorem holds. With applications in quantum information theory in mind sufficient conditions are given for a trace preserving, positive map on J1, the space of trace class operators, to have a unique, stric...

Admissible Arrays and a Nonlinear Generalization of Perron-frobenius Theory

Let Kn ̄2x `2n :x i & 0 for 1% i% n ́ and suppose that f :Kn MNKn is nonexpansive with respect to the F " -norm and f(0) ̄ 0. It is known that for every x `Kn there exists a periodic point ξ ̄ ξ x `Kn (so f p(ξ ) ̄ ξ for some minimal positive integer p ̄ pξ) and f k(x) approaches 2 f j(ξ ) :0% j! p ́ as k approaches infinity. What can be said about P*(n), the set of positive integers p for which there...

Weighted Frobenius-Perron and Koopman operators