  We study perturbations of a partially hyperbolic toral automorphism L which
is diagonalizable over C and has a dense center foliation. For a small
perturbation of L with a smooth center foliation we establish existence of a
smooth leaf conjugacy to L. We also show that if a small perturbation of an
ergodic irreducible L has smooth center foliation and is bi-Holder conjugate to
L, then the conjugacy is smooth. As a corollary, we show that for any
symplectic perturbation of such an L any bi-Holder conjugacy must be smooth.
For a totally irreducible L with two-dimensional center, we establish a number
of equivalent conditions on the perturbation that ensure smooth conjugacy to L.
