UNCONDITIONAL BASES OF INVARIANT SUBSPACES OF A CONTRACTION WITH FINITE DEFECTS

SERGUEI TREIL

Abstract. 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) < ∞, rank(I − T T^{∗}) < ∞) 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.