We suggest an approach for finding the maximal and the minimal spectral radius of linear operators from a given compact family of operators, which share a common invariant cone (e.g. family of nonnegative matrices). In the case of families with so-called product structure, this leads to efficient algorithms for optimizing the spectral radius and for finding the joint and lower spectral radii of...

Let T be a measure-preserving transformation acting on a probability space (a, Sr, P). This T induces a linear isometry V on &(a, F, P) defined by V(f) = f o T. The analysis of T by using properties of V is referred to as spectral analysis. It is often profitable to consider the action of V on certain closed linear invariant subspaces 9 of L,(O, ST, P). In this note we make the following assump...