UNCONDITIONAL BASES OF INVARIANT SUBSPACES OF A CONTRACTION WITH FINITE DEFECTS

The main result of the paper is that a system of invariant subspaces o f a (completely non-unitary) Hilbert space contraction T with finite d efects (rank(I - TT) < infinity, rank(I - TT*) < infinity) is an unco nditional 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 in terpolation theorem. For general invariant subspaces of operators with defects 1-1 such theorem was proved by V. I. Vasyunin. Then partial r esults for the case of finite defects were obtained by the author. The present paper solves the problem completely.