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arXiv · 0908.3805

A noncommutative version of the Fej\'er-Riesz theorem

Yurii Savchuk·Konrad Schmüdgen
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Abstract

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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Yurii Savchuk, Konrad Schmüdgen. 2009-08-26. A noncommutative version of the Fej\'er-Riesz theorem. https://arxiv.org/abs/0908.3805

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