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

Thu, 08/27/2009 - 13:23 — SomNambul
Authors: Yurii Savchuk, Konrad Schmüdgen
Subjects: Operator Algebras
link: http://arxiv.org/abs/0908.3805
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 $X=Y^*Y$.