In [Ko 2] we extend Putinar's theorem to every operator on a finite dimensional space by generalizing Putinar's techniques. Using these techniques, we construct a functional model for the unilateral backward shift. We show, in particular, that the unilateral backward shift is w-quasisubscalar. As a corollary we prove that every strict contraction is w-subscalar, i.e., is similar to the restriction to an invariant subspace of a w-scalar operator.
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*Research partially supported by GARC.