Unconditional bases of invariant subspaces of a contraction with finite defects
Serguei Treil
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$(I-T^*T) \lt \infty$, rank$(I-TT^*) \lt \infty$) 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.