POSITIVE BLOCK MATRICES
Year
: 2017
Abstract: Let $C$ and $D$ be positive operators such that $C\\leq D$ and $D$ be invertible. We show that there exists a trace preserving unital completely positive map $\\Phi_{C,D}:\\mathbb{B}(\\mathcal{H})\\rightarrow \\mathbb{B}(\\mathcal{H})$ such that the block operator matrices
\\begin{equation*}
\\left(
\\begin{array}{cc}
\\Phi_{C,D}(A) & C \\\\
C & \\Phi_{C,D}(B) \\\\
\\end{array}
\\right)
\\end{equation*}
are positive, for all positive operators $A$ and $B$ such that $D=A\\sharp B$.
\\begin{equation*}
\\left(
\\begin{array}{cc}
\\Phi_{C,D}(A) & C \\\\
C & \\Phi_{C,D}(B) \\\\
\\end{array}
\\right)
\\end{equation*}
are positive, for all positive operators $A$ and $B$ such that $D=A\\sharp B$.
Keyword(s): Geometric mean,Positive block matrix,Completely positive linear map
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POSITIVE BLOCK MATRICES
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| contributor author | حامد نجفی | en |
| contributor author | Hamed Najafi | fa |
| date accessioned | 2020-06-06T14:25:46Z | |
| date available | 2020-06-06T14:25:46Z | |
| date copyright | 3/8/2017 | |
| date issued | 2017 | |
| identifier uri | http://libsearch.um.ac.ir:80/fum/handle/fum/3396274?locale-attribute=en | |
| description abstract | Let $C$ and $D$ be positive operators such that $C\\leq D$ and $D$ be invertible. We show that there exists a trace preserving unital completely positive map $\\Phi_{C,D}:\\mathbb{B}(\\mathcal{H})\\rightarrow \\mathbb{B}(\\mathcal{H})$ such that the block operator matrices \\begin{equation*} \\left( \\begin{array}{cc} \\Phi_{C,D}(A) & C \\\\ C & \\Phi_{C,D}(B) \\\\ \\end{array} \\right) \\end{equation*} are positive, for all positive operators $A$ and $B$ such that $D=A\\sharp B$. | en |
| language | English | |
| title | POSITIVE BLOCK MATRICES | en |
| type | Conference Paper | |
| contenttype | External Fulltext | |
| subject keywords | Geometric mean | en |
| subject keywords | Positive block matrix | en |
| subject keywords | Completely positive linear map | en |
| identifier link | https://profdoc.um.ac.ir/paper-abstract-1063636.html | |
| conference title | سومین سمینار نظریه عملگرها و کاربردهای آن | fa |
| conference location | مشهد | fa |
| identifier articleid | 1063636 |