PERRON-FROBENIUS THEORY FOR FINITE-DIMENSIONAL SPACES WITH A HYPERBOLIC CONE

If X is a real n-dimensional space provided with a subnorm pi, then th e inequality xi greater than or equal to pi(x) defines a so-called hyp erbolic cone in E = R + X. In this case the Perron-Frobenius theory ad mits some special features. A relevant characterization of nonnegative operators in a matrix form is given first. Auxiliary information from spectral theory and from the geometry of subnormed spaces is collecte d as preparation.