Factoring a Quadratic Operator as a Product of Two Positive Contractions
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Let T be a quadratic operator on a complex Hilbert space H. We show that T can be written as a product of two positive contractions if and only if T is of the form aI circle plus bI circle plus [GRAPHICS] on H-1 circle plus H-2 circle plus (H-3 circle plus H-3) for some a, b is an element of [0, 1] and strictly positive operator P with parallel to P parallel to <= vertical bar root a - root b vertical bar root(1 - a) (1 - b). Also, we give a necessary condition for a bounded linear operator T with operator matrix [GRAPHICS] on H circle plus K that can be written as a product of two positive contractions.
Li, Chi-Kwong and Tsai, Ming-Cheng, Factoring a Quadratic Operator as a Product of Two Positive Contractions (2016).