Factoring a Quadratic Operator as a Product of Two Positive Contractions

Chi Kwong Li; Ming Cheng Tsai

doi:10.4153/CMB-2015-049-4

Factoring a Quadratic Operator as a Product of Two Positive Contractions

Chi Kwong Li
, Ming Cheng Tsai

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研究成果: 期刊貢獻 › 文章 › 同行評審

1 引文斯高帕斯（Scopus）

摘要

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 (Equation presented) for some a,b ∈ [0,1] and strictly positive operator P with ||P|| ≤|√ a, √ b|√(1, a)(1-b). Also, we give a necessary condition for a bounded linear operator T with operator matrix (equation presented) on H ⊕ K that can be written as a product of two positive contractions.

原文	English
頁（從 - 到）	354-362
頁數	9
期刊	Canadian Mathematical Bulletin
卷	59
發行號	2
DOIs	https://doi.org/10.4153/CMB-2015-049-4
出版狀態	Published - 6月 2016

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© Canadian Mathematical Society 2016.

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N2 - 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 (Equation presented) for some a,b ∈ [0,1] and strictly positive operator P with ||P|| ≤|√ a, √ b|√(1, a)(1-b). Also, we give a necessary condition for a bounded linear operator T with operator matrix (equation presented) on H ⊕ K that can be written as a product of two positive contractions.

AB - 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 (Equation presented) for some a,b ∈ [0,1] and strictly positive operator P with ||P|| ≤|√ a, √ b|√(1, a)(1-b). Also, we give a necessary condition for a bounded linear operator T with operator matrix (equation presented) on H ⊕ K that can be written as a product of two positive contractions.

KW - Positive contraction

KW - Quadratic operator

KW - Spectral theorem

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Factoring a Quadratic Operator as a Product of Two Positive Contractions

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