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A strict Positivstellensatz for the Weyl algebra

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Abstract.

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.

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  1. Fakultät für Mathematik und Informatik, Universität Leipzig, Augustusplatz 10, 04109, Leipzig, Germany

    Konrad Schmüdgen

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  1. Konrad Schmüdgen
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Correspondence to Konrad Schmüdgen.

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Mathematics Subject Classification (2000): 11 E25, 14 P10, 47 L60, 16 W10

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Schmüdgen, K. A strict Positivstellensatz for the Weyl algebra. Math. Ann. 331, 779–794 (2005). https://doi.org/10.1007/s00208-004-0604-4

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  • DOI: https://doi.org/10.1007/s00208-004-0604-4

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