  The main result of the paper is that a system of invariant subspaces of a
(completely non-unitary) Hilbert space contraction $T$ with finite defects
(rank$(I-T^*T)<\infty$, rank$(I-TT^*)<\infty$) is an unconditional basis (Riesz
basis) if and only if it is uniformly minimal.
  Results of such type are quite well known: for a system of eigenspaces of a
contraction with defects $1-1$ it is simply the famous Carleson interpolation
theorem. For general invariant subspaces of operators with defects $1-1$ such
theorem was proved by V. I. Vasyunin. Then partial results for the case of
finite defects were obtained by the author.
  The present paper solves the problem completely.
