A Strict Positivstellensatz for the Weyl Algebra
Abstract
Description
Let $c$ be an element of the Weyl algebra $W(d)$ which is given by a strictly positive operator in the Schr"odinger representation. It is shown that, under some conditions, there exist elements $b_1,...,b_d$ in $W(d)$ such that $b_1 c b_1^* + ... + b_d c b_d^*$ is a finite sum of squares.
17 pages, condition (i) in Theorem 1.1 implies (ii). Assumption (ii) can be omitted
17 pages, condition (i) in Theorem 1.1 implies (ii). Assumption (ii) can be omitted