A noncommutative version of the Fejér-Riesz theorem

preprint2010arXivOpen access

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∗YX=Y^*Y.

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