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RISUffe Haagerup His life and mathematics
In remembrance of Professor Uffe Valentin Haagerup -1949–2015-,
as a brilliant mathematician, we review some aspects of his life, and his outstanding
mathematical accomplishments....
Haagerup--Pisier--Ringrose inequality
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...
|\\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_...
|X_1 \\oplus \\cdots\\oplus X_n...
|\\, \\|\\Phi\\|^2\\left\\|\\sum_{j=1}^n A_j^2\\right\\|.
\\end{align*}...
An Operator Inequality for Bounded Linear Maps Between $$C^*$$ C ∗
( |A_k|^2+|A_k^*|^2 right) right |
end{equation*}
for all $n in mathbb{N}$ and all $A_1, ldots, A_n in mathscr{A}$. This improves the Haagerup--Pisier--Ringrose (H-P-R) inequality for Hermitian bounded maps Phi. In addition, we...