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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.

To obtain the paper, click on your choice below.

*Serguei Treil *

Mon Jan 8 18:13:32 EST 1996