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>