Haagerup--Pisier--Ringrose inequality
سال
: 2018
چکیده: The Haagerup--Pisier--Ringrose inequality states that if $\\Phi$ is a bounded linear map from a $C^*$-algebra $\\mathscr{A}$ into a $C^*$-algebra $\\mathscr{B}$, then
\\begin{align}\\label{HPR}
\\left\\|\\sum_{j=1}^n\\left\\{\\Phi(A_j)^* \\Phi(A_j)+\\Phi(A_j) \\Phi(A_j)^*\\right\\} \\right\\|\\leq K\\|\\Phi\\|^2 \\left\\|\\sum_{j=1}^n\\left(\\sqsq{A_j}\\right)\\right\\|
\\end{align}
holds for $K=4$ and for any finite family $\\{A_1, \\cdots, A_n\\}$ of elements of $\\mathscr{A}$. In this talk, we present several versions of the Haagerup--Pisier--Ringrose inequality involving unitarily invariant norms and unital completely positive maps. Among other things, we show that if $\\mathcal{J}$ is the ideal of $\\mathbb{B}(\\mathscr{H})$ associated to a unitarily invariant norm $ |\\cdot |$, $\\Phi: \\mathscr{A} \\to \\mathscr{B}$ is a bounded linear map between $C^*$-algebras, $A_1, \\cdots, A_n\\in \\mathscr{A}$ are positive such that $\\Phi(A_j)$'s commute for $1\\leq j\\leq n$ and $X_1, \\cdots, X_n \\in \\mathcal{J}$. Then
\\begin{align*}
\\left|\\left|\\left| \\sum_{j=1}^n\\left\\{ \\Phi(A_j)X_j\\Phi(A_j)^*+\\Phi(A_j)^*X_j\\Phi(A_j)\\right\\}\\right|\\right|\\right|\\leq 4 |X_1 \\oplus \\cdots\\oplus X_n |\\, \\|\\Phi\\|^2\\left\\|\\sum_{j=1}^n A_j^2\\right\\|.
\\end{align*}
\\begin{align}\\label{HPR}
\\left\\|\\sum_{j=1}^n\\left\\{\\Phi(A_j)^* \\Phi(A_j)+\\Phi(A_j) \\Phi(A_j)^*\\right\\} \\right\\|\\leq K\\|\\Phi\\|^2 \\left\\|\\sum_{j=1}^n\\left(\\sqsq{A_j}\\right)\\right\\|
\\end{align}
holds for $K=4$ and for any finite family $\\{A_1, \\cdots, A_n\\}$ of elements of $\\mathscr{A}$. In this talk, we present several versions of the Haagerup--Pisier--Ringrose inequality involving unitarily invariant norms and unital completely positive maps. Among other things, we show that if $\\mathcal{J}$ is the ideal of $\\mathbb{B}(\\mathscr{H})$ associated to a unitarily invariant norm $
\\begin{align*}
\\left|\\left|\\left| \\sum_{j=1}^n\\left\\{ \\Phi(A_j)X_j\\Phi(A_j)^*+\\Phi(A_j)^*X_j\\Phi(A_j)\\right\\}\\right|\\right|\\right|\\leq 4
\\end{align*}
کلیدواژه(گان): Haagerup--Pisier--Ringrose inequality,unitarily invariant norm,C*-algebra
کالکشن
:
-
آمار بازدید
Haagerup--Pisier--Ringrose inequality
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| contributor author | محمد صال مصلحیان | en |
| contributor author | Mohammad Sal Moslehian | fa |
| date accessioned | 2020-06-06T14:28:25Z | |
| date available | 2020-06-06T14:28:25Z | |
| date copyright | 8/1/2018 | |
| date issued | 2018 | |
| identifier uri | https://libsearch.um.ac.ir:443/fum/handle/fum/3398149 | |
| description abstract | The Haagerup--Pisier--Ringrose inequality states that if $\\Phi$ is a bounded linear map from a $C^*$-algebra $\\mathscr{A}$ into a $C^*$-algebra $\\mathscr{B}$, then \\begin{align}\\label{HPR} \\left\\|\\sum_{j=1}^n\\left\\{\\Phi(A_j)^* \\Phi(A_j)+\\Phi(A_j) \\Phi(A_j)^*\\right\\} \\right\\|\\leq K\\|\\Phi\\|^2 \\left\\|\\sum_{j=1}^n\\left(\\sqsq{A_j}\\right)\\right\\| \\end{align} holds for $K=4$ and for any finite family $\\{A_1, \\cdots, A_n\\}$ of elements of $\\mathscr{A}$. In this talk, we present several versions of the Haagerup--Pisier--Ringrose inequality involving unitarily invariant norms and unital completely positive maps. Among other things, we show that if $\\mathcal{J}$ is the ideal of $\\mathbb{B}(\\mathscr{H})$ associated to a unitarily invariant norm $ | en |
| description abstract | |\\cdot | en |
| description abstract | |$, $\\Phi: \\mathscr{A} \\to \\mathscr{B}$ is a bounded linear map between $C^*$-algebras, $A_1, \\cdots, A_n\\in \\mathscr{A}$ are positive such that $\\Phi(A_j)$'s commute for $1\\leq j\\leq n$ and $X_1, \\cdots, X_n \\in \\mathcal{J}$. Then \\begin{align*} \\left|\\left|\\left| \\sum_{j=1}^n\\left\\{ \\Phi(A_j)X_j\\Phi(A_j)^*+\\Phi(A_j)^*X_j\\Phi(A_j)\\right\\}\\right|\\right|\\right|\\leq 4 | en |
| description abstract | |X_1 \\oplus \\cdots\\oplus X_n | en |
| description abstract | |\\, \\|\\Phi\\|^2\\left\\|\\sum_{j=1}^n A_j^2\\right\\|. \\end{align*} | en |
| language | English | |
| title | Haagerup--Pisier--Ringrose inequality | en |
| type | Conference Paper | |
| contenttype | External Fulltext | |
| subject keywords | Haagerup--Pisier--Ringrose inequality | en |
| subject keywords | unitarily invariant norm | en |
| subject keywords | C*-algebra | en |
| identifier link | https://profdoc.um.ac.ir/paper-abstract-1068986.html | |
| identifier articleid | 1068986 |