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PERRON-FROBENIUS THEORY ON THE NUMERICAL RANGE FOR SOME CLASSES OF REAL MATRICES

We give further results for Perron-Frobenius theory on the numericalrange of real matrices and some other results generalized from nonnegative matricesto real matrices. We indicate two techniques for establishing the main theorem ofPerron and Frobenius on the numerical range. In the rst method, we use acorresponding version of Wielandt's lemma. The second technique involves graphtheory.

Some results on the block numerical range

The main results of this paper are generalizations of classical results from the numerical range to the block numerical range. A different and simpler proof for the Perron-Frobenius theory on the block numerical range of an irreducible nonnegative matrix is given. In addition, the Wielandt's lemma and the Ky Fan's theorem on the block numerical range are extended.

Compact weighted Frobenius-Perron operators and their spectra

In this note we characterize the compact weighted Frobenius-Perron operator $p$ on $L^1(Sigma)$ and determine their spectra. We also show that every weakly compact weighted Frobenius-Perron operator on $L^1(Sigma)$ is compact.

Weighted Frobenius-Perron and Koopman operators

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...