A noncommutative version of the Fej\'er-Riesz theorem
classification
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math.FA
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operatoralgebraelementer-rieszgeneratednoncommutativenonnegativeshift
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Let $\cX$ be the unital *-algebra generated by the unilateral shift operator. It is shown that for any nonnegative operator $X\in \cX$ there is an element $Y\in \cX$ such that $X=Y^*Y$.
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