相关论文: A Note on the p->q norms of Completely Positive Ma…

Let $f$ be an operator convex function on $(0,\infty)$, and $\Phi$ be a unital positive linear maps on $B(H)$. we give a complementary inequality to Davis-Choi-Jensen's inequality as follows \begin{equation*} f(\Phi(A))\geq…

We present an alternative (constructive) proof of the statement that for every completely positive, trace-preserving map $\Phi$ there exists an auxiliary Hilbert space $\mathcal K$ in a pure state $|\psi\rangle\langle\psi|$ as well as a…

A linear map $\Phi :\mathbb{M}_n \to \mathbb{M}_k$ is called completely copositive if the resulting matrix $[\Phi (A_{j,i})]_{i,j=1}^m$ is positive semidefinite for any integer $m$ and positive semidefinite matrix $[A_{i,j}]_{i,j=1}^m$. In…

We prove that a unital completely positive map between finite-dimensional C*-algebras is a homomorphism if and only if it is completely entropy-nonincreasing, where the relevant notion of entropy is a variant of von Neumann entropy. This…

Assuming a unitarily invariant norm $|||\cdot|||$ is given on a two-sided ideal of bounded linear operators acting on a separable Hilbert space, it induces some unitarily invariant norms $|||\cdot|||$ on matrix algebras $\mathcal{M}_n$ for…

Let $A,B\in \mathbb{B}(\mathscr{H})$ be such that $0<b_{1}I \leq A \leq a_{1}I$ and $0<b_{2}I \leq B \leq a_{2}I$ for some scalars $0<b_{i}< a_{i},\;\; i=1,2$ and $\Phi:\mathbb{B}(\mathscr{H})\rightarrow\mathbb{B}(\mathscr{K})$ be a…

Let $\Phi=(G,U(\mathbb{Q}),\varphi)$ be a quaternion unit gain graph (or $U(\mathbb{Q})$-gain graph) of order $n$, $A(\Phi)$ be the adjacency matrix of $\Phi$ and $r(\Phi)$ be the row left rank of $\Phi$. Let $\Delta$ be the maximum degree…

The dual of a matrix ordered space has a natural matrix ordering that makes the dual space matrix ordered as well. The purpose of these notes is to give a condition that describes when the linear map taking a basis of the n by n matrices to…

The paper is devoted to the problem of classification of extremal positive maps acting between $B(K)$ and $B(H)$ where $K$ and $H$ are Hilbert spaces. It is shown that every positive map with the property that $\rank \phi(P)\leq 1$ for any…

A linear map between matrix spaces is positive if it maps positive semidefinite matrices to positive semidefinite ones, and is called completely positive if all its ampliations are positive. In this article quantitative bounds on the…

Given a sequence of bounded operators $a_j$ on a Hilbert space $H$ with $\sum a_j^*a_j=1=\sum a_ja_j^*$, we study the map $\Psi$ defined on $B(H)$ by $\Psi(x)=\sum a_j^*xa_j$ and its restriction $\Phi$ to the Hilbert-Schmidt class $C^2(H)$.…

We present a general characterization of k-positivity for a positive map in terms of the estimation of the Ky Fan norm of the matrix constructed from the Kraus operators of the associated completely positive map. Combining this with the…

Given a Fourier-Mukai functor $\Phi$ in the general setting of singular schemes, under various hypotheses we provide both left and a right adjoints to $\Phi$, and also give explicit formulas for them. These formulas are simple and natural,…

We show that for every "locally finite" unit-preserving completely positive map P acting on a C*-algebra, there is a corresponding *-automorphism \alpha of another unital C*-algebra such that the two sequences P, P^2,P^3,... and \alpha,…

This article proves the existence of completely positive quasimultiplicative maps from the group algebra of imprimitive reflection groups to the set of bounded operators, and uses those linear maps to define creation and annihilation…

Let $\phi$ be a linear map from the $n\times n$ matrices ${\mathcal M}_n$ to the $m\times m$ matrices ${\mathcal M}_m$. It is known that $\phi$ is $2$-positive if and only if for all $K\in {\mathcal M}_n$ and all strictly positive $X\in…

We study operators of the form X+Y where Y has a finite p-th Schatten norm (p<2), and X is self-adjoint and of Hilbert-Schmidt class. Our study is based on new theorems on zero distribution of entire functions of finite order.

We consider the class of integral operators $Q_\f$ on $L^2(\R_+)$ of the form $(Q_\f f)(x)=\int_0^\be\f (\max\{x,y\})f(y)dy$. We discuss necessary and sufficient conditions on $\phi$ to insure that $Q_{\phi}$ is bounded, compact, or in the…

Let $\mathscr{A}$ be a unital $C^*$-algebra and let $\Phi: \mathscr{A} \to {\mathbb B}({\mathscr H})$ be a unital $n$-positive linear map between $C^*$-algebras for some $n \geq 3$. We show that $$\|\Phi(AB)-\Phi(A)\Phi(B)\| \leq…

Given an $n \times d$ matrix $A$, its Schatten-$p$ norm, $p \geq 1$, is defined as $\|A\|_p = \left (\sum_{i=1}^{\textrm{rank}(A)}\sigma_i(A)^p \right )^{1/p}$, where $\sigma_i(A)$ is the $i$-th largest singular value of $A$. These norms…