A strict Positivstellensatz for the Weyl algebra

Let c be an element of the Weyl algebra which is given by a strictly positive operator in the Schrödinger representation. It is shown that, under some conditions, there exist certain elements b₁,...,b_d from such that ^d_j=1 b_j c b*_j is a finite sum of squares.Mathematics Subject Classification (2000): 11 E25, 14 P10, 47 L60, 16 W10