A Strict Positivstellensatz for the Weyl Algebra

Details A Strict Positivstellensatz for the Weyl Algebra A Strict Positivstellensatz for the Weyl Algebra

2004-03-03

arxiv.org/abs/math/0403076v2

Math. Annalen 331 (2005), pp. 779-794

Mathematics

Algebraic Geometry

17 pages, condition (i) in Theorem 1.1 implies (ii). Assumption (ii) can be omitted

Scientific paper

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.

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