We have an ergodic measure preserving system such that there is an orthonormal basis for $L^2$ which consists of eigenfunctions of T. This is just a definition of discrete spectrum ergodic system.
How can I show that there is a sequence ${n_k}$ of integers such that $||{T^{n_k}f-f}||_2$ goes to zero for $f \in L^2$?
Any hint or answer would be appreciated. Also, is the added assumption of ergodicity needed?