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Proceedings of the American Mathematical Society

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Flat extensions in $ \ast$-algebras


Authors: Bernard Mourrain and Konrad Schmüdgen
Journal: Proc. Amer. Math. Soc. 144 (2016), 4873-4885
MSC (2010): Primary 46L05; Secondary 44A60
Published electronically: May 3, 2016
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Abstract: The main result of the paper is a flat extension theorem for positive linear functionals on $ *$-algebras. The theorem is applied to truncated moment problems on cylinder sets, on matrices of polynomials and on enveloping algebras of Lie algebras.


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Additional Information

Bernard Mourrain
Affiliation: Inria Sophia Antipolis Méditerranée, BP 93, 06902 Sophia Antipolis, France
Email: Bernard.Mourrain@inria.fr

Konrad Schmüdgen
Affiliation: Mathematisches Institut, Universität Leipzig, Augustusplatz 10/11, D-04109 Leipzig, Germany
Email: schmuedgen@math.uni-leipzig.de

DOI: https://doi.org/10.1090/proc/13158
Keywords: $\ast$-algebras, flat extension, hermitian linear form, GNS construction, truncated moment problem, enveloping algebra
Received by editor(s): July 9, 2014
Received by editor(s) in revised form: January 18, 2016
Published electronically: May 3, 2016
Communicated by: Harm Derksen
Article copyright: © Copyright 2016 by the authors