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A noncommutative version of the Fejér-Riesz theorem
Author(s):
Yuriĭ
Savchuk;
Konrad
Schmüdgen
Journal:
Proc. Amer. Math. Soc.
138
(2010),
1243-1248.
MSC (2000):
Primary 14A22, 47A68;
Secondary 42A05
Posted:
December 2, 2009
MathSciNet review:
2578518
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Abstract:
Let  be the unital  -algebra generated by the unilateral shift operator. It is shown that for any nonnegative operator  there is an element  such that  .
References:
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- M. Dritschel, Rovnyak, J., The operator Fejér-Riesz theorem, arXiv: 0903.3639v1.
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- K. Schmüdgen, Noncommutative real algebraic geometry - some basic concepts and first ideas, in: Emerging applications of algebraic geometry, M. Putinar and S. Sullivant (eds.), Springer, New York, 2009. MR 2500470
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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:
10.1090/S0002-9939-09-10215-0
PII:
S 0002-9939(09)10215-0
Keywords:
Fej\'er-Riesz theorem,
noncommutative Positivstellensatz,
Toeplitz algebra.
Received by editor(s):
August 26, 2009
Posted:
December 2, 2009
Communicated by:
Nigel J. Kalton
Copyright of article:
Copyright
2009,
American Mathematical Society
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