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

General Education Center

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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 (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.

Original language	English
Pages (from-to)	354-362
Number of pages	9
Journal	Canadian Mathematical Bulletin
Volume	59
Issue number	2
DOIs	https://doi.org/10.4153/CMB-2015-049-4
State	Published - Jun 2016

Bibliographical note

Publisher Copyright:
© Canadian Mathematical Society 2016.

Keywords

Positive contraction
Quadratic operator
Spectral theorem

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10.4153/CMB-2015-049-4

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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

Abstract

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Keywords

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