## Document Type

Article

## Department/Program

Mathematics

## Journal Title

Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques

## Pub Date

2016

## Volume

59

## Issue

2

## First Page

354

## 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.

## Recommended Citation

Li, Chi-Kwong and Tsai, Ming-Cheng, Factoring a Quadratic Operator as a Product of Two Positive Contractions (2016). *Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques*, 59(2), 354-362.

10.4153/CMB-2015-049-4

## DOI

10.4153/CMB-2015-049-4