Abstract
If A and B are contraction operators on a Hilbert space \({\mathcal{H}}\) that commute with a shift operator S, it is shown that A = BC for some contraction operator C on \({\mathcal{H}}\) that commutes with S if and only if \({AA^{*} \leq BB^{*}}\).
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Leech, R.B. Factorization of Analytic Functions and Operator Inequalities. Integr. Equ. Oper. Theory 78, 71–73 (2014). https://doi.org/10.1007/s00020-013-2107-8
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DOI: https://doi.org/10.1007/s00020-013-2107-8