A noncommutative version of the Fejér-Riesz theorem

Savchuk, Yuriĭ; Schmüdgen, Konrad

doi:10.1090/S0002-9939-09-10215-0

A noncommutative version of the Fejér-Riesz theorem
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by Yuriĭ Savchuk and Konrad Schmüdgen PDF

Proc. Amer. Math. Soc. 138 (2010), 1243-1248 Request permission

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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