Perron roots of a convex combination of a cone preserving map and its adjoint (Q762241)

The author considers generalizations of the result of Levinger and Fiedler that for a square matrix A of nonnegative real numbers, the Perron root r(t) of \((1-t)A+tA^*\) as a function of t is non-decreasing for \(t\in (0,)\) and non-increasing for \(t\in (,1).\) The setting is an operator which together with its adjoint leaves invariant a cone in an inner product space. A result similar to the Levinger-Fiedler result is obtained if the cone induces a Riesz space structure and some further natural conditions on the operator and the cone are satisfied.