Algebras of fractions and strict Positivstellensatze for *-algebras

作者：Schmuedgen Konrad

来源：Journal fur die Reine und Angewandte Mathematik, 2010, 647: 57-86.

DOI：10.1515/CRELLE.2010.073

In this paper we investigate a *-algebra X of fractions associated with a unital complex *-algebra A. The *-algebra X and its Hilbert space representations are used to prove abstract noncommutative strict Positivstellensatze for A. Multi-grading of A are studied as technical tools to verify the assumptions of this theorem.
As applications we obtain new strict Positivstellensatze for the Weyl algebra and for the Lie algebra g of the affine group of the real line. We characterize integrable representations of the Lie algebra g in terms of resolvents of the generators and derive a new integrability criterion for representations of g.

• 出版日期2010-10