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  • One lets P = sqrt(A A^*) (I think)> and then A = O P , where O is an isometry or a partial> isometry and P is a so-called positive operator.> This might seem like a promising divide-and-conquer> approach to the invariant sub-space problem, but> it does not seem to say much about what happens when,> starting with a non-zero x in H, one iterates> A, constructing Ax, AAx, A^3 x, etc or using> the po
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