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Unconditional bases of invariant subspaces of a contraction with finite defects

by 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 (, ) 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.

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Serguei Treil
Mon Jan 8 18:13:32 EST 1996