On Polynomially Bounded Weighted Shifts, Ii
نویسنده
چکیده
Let T be an operator-weighted shift whose weights are 2-by-2 matrices. We say that, given > 0, T is in the -canonical form if each weight is an upper triangular matrix (aij), with 0 ≤ a11, a22 ≤ 1 and a12 6= 0 implies a11, a22 < . We generalize this concept to operator-weighted shifts whose weights are n-by-n matrices and we show that every polynomially bounded weighted shift, whose weights are finite-dimensional matrices of the fixed dimension n, is similar to an operator in the -canonical form. This enables us to prove that every polynomially bounded weihghted shift with finite dimensional weights is similar to a contraction.
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