English

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

Operator Algebras 2010-07-07 v2 Functional Analysis

Abstract

Let \cX\cX be the unital *-algebra generated by the unilateral shift operator. It is shown that for any nonnegative operator X\cXX\in \cX there is an element Y\cXY\in \cX such that X=YYX=Y^*Y.

Keywords

Cite

@article{arxiv.0908.3805,
  title  = {A noncommutative version of the Fej\'er-Riesz theorem},
  author = {Yurii Savchuk and Konrad Schmüdgen},
  journal= {arXiv preprint arXiv:0908.3805},
  year   = {2010}
}