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A noncommutative version of the Fejér-Riesz theorem


Authors: Yuriĭ Savchuk and Konrad Schmüdgen
Journal: Proc. Amer. Math. Soc. 138 (2010), 1243-1248
MSC (2000): Primary 14A22, 47A68; Secondary 42A05
DOI: https://doi.org/10.1090/S0002-9939-09-10215-0
Published electronically: December 2, 2009
MathSciNet review: 2578518
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $ \mathcal{X}$ be the unital $ *$-algebra generated by the unilateral shift operator. It is shown that for any nonnegative operator $ X\in \mathcal{X}$ there is an element $ Y\in \mathcal{X}$ such that $ X=Y^*Y$.


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Additional Information

Yuriĭ Savchuk
Affiliation: Mathematisches Institut, Universität Leipzig, Johannisgasse 26, 04103 Leipzig, Germany
Email: savchuk@math.uni-leipzig.de

Konrad Schmüdgen
Affiliation: Mathematisches Institut, Universität Leipzig, Johannisgasse 26, 04103 Leipzig, Germany
Email: schmuedgen@math.uni-leipzig.de

DOI: https://doi.org/10.1090/S0002-9939-09-10215-0
Keywords: Fej\'er-Riesz theorem, noncommutative Positivstellensatz, Toeplitz algebra.
Received by editor(s): August 26, 2009
Published electronically: December 2, 2009
Communicated by: Nigel J. Kalton
Article copyright: © Copyright 2009 American Mathematical Society

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