Bounding functions for Markov decision processes in relation to the spectral radius

We consider Markov decision processes in the situation of discrete time, countable state space and general decision space. By introducing so-called "weighted supremum norms" or "bounding functions", convergence of successive approximations to the value function can be proved under certain conditions. These bounding functions may also be applied to reduce the norms of the transition probability matrices and hence (mostly) to improve upper and lower bounds of the approximation procedure. In this paper we will show, that it is possible to construct bounding functions which are strongly excessive with an excessivity factor arbitrarily close to the spectral radius of the Markov decision process, where this spectral radius is assumed to be smaller than one.