Perron-Frobenius Type Results on the Numerical Range

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.

A primer of Perron–Frobenius theory for matrix polynomials

We present an extension of Perron–Frobenius theory to the spectra and numerical ranges of Perron polynomials, namely, matrix polynomials of the form L(λ) = Iλ − Am−1λm−1 − · · · − A1λ− A0, where the coefficient matrices are entrywise nonnegative. Our approach relies on the companion matrix linearization. First, we recount the generalization of the Perron–Frobenius Theorem to Perron polynomials ...

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.

Spectrum Properties of the Koopman and Frobenius-Perron Operators