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Factoring a Quadratic Operator as a Product of Two Positive Contractions
Li, Chi-Kwong Tsai, Ming-Cheng
Li, Chi-Kwong
Tsai, Ming-Cheng
Abstract
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.
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2016-01-01
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Mathematics
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10.4153/CMB-2015-049-4