Some remarks on the asymptotic behaviour of the iterates of a bounded linear operator
We discuss the problem of characterizing the possible asymptotic behaviour of the norm of the iterates of a bounded linear operator between two Banach spaces. In particular, given an increasing sequence of positive numbers tending to infinity, we construct Banach spaces such that the norm of the iterates of a suitable multiplication operator between these spaces assumes (or exceeds) the values of this sequence.