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Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Cuntz, Joachim / Huybrechts, Daniel / Hwang, Jun-Muk

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Volume 2010, Issue 647 (Jan 2010)


Algebras of fractions and strict Positivstellensätze for ∗-algebras

Konrad Schmüdgen
Published Online: 2010-10-21 | DOI: https://doi.org/10.1515/CRELLE.2010.073


In this paper we investigate a ∗-algebra 𝔛 of fractions associated with a unital complex ∗-algebra . The ∗-algebra 𝔛 and its Hilbert space representations are used to prove abstract noncommutative strict Positivstellensätze for . Multi-grading of are studied as technical tools to verify the assumptions of this theorem.

As applications we obtain new strict Positivstellensätze for the Weyl algebra and for the Lie algebra of the affine group of the real line. We characterize integrable representations of the Lie algebra in terms of resolvents of the generators and derive a new integrability criterion for representations of .

About the article

Received: 2009-03-16

Revised: 2009-05-15

Published Online: 2010-10-21

Published in Print: 2010-10-01

Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal), ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: https://doi.org/10.1515/CRELLE.2010.073. Export Citation

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