Perron-Frobenius theory for finite-dimensional spaces with a hyperbolic cone Original Research Article

If X is a real n-dimensional space provided with a subnorm π, then the inequality ξ greater-or-equal, slanted π(x) defines a so-called hyperbolic cone inE =Rcircled plus X. In this case the Perron-Frobenius theory admits 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 collected as preparation.