Iteration of linear p-norm nonexpansive maps

In this paper we will examine the asymptotic behaviour of the iterates of linear maps that are nonexpansive (contractive) with respect to a classical p-norm on . As a main result it will be shown that if 1 p ∞ and p≠2, there exists an integer q 1 such that the sequence (Akqx)k is convergent for each . Moreover the integer q is the order, or twice the order, of a permutation on n letters.