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

We introduce a noncommutative analogue of the absolute value of a regular operator acting on a noncommutative $\mathrm{L}^p$-space. We equally prove that two classical operator norms, the regular norm and the decomposable norm are…

Given a class Phi of weights, we study the following classes: Phi^+ of Phi-flat weights which are the psi for which psi-colimits commute in the base V with limits with weights in Phi; and Phi^-, dually defined, of weights psi for which…

The aim of this paper is twofold. First, we obtain a Schwarz-Pick type lemma for the $\alpha$-harmonic mapping $u=P_{\alpha}[\phi]$, where $\phi\in L^{p}(\mathbb{S}^{n-1},\mathbb{R} )$ and $p\in[1,\infty]$. We get an explicit form of the…

The algebraic mapping torus $M_{\Phi}$ of a group $G$ with an automorphism $\Phi$ is the HNN-extension of $G$ in which conjugation by the stable letter performs $\Phi$. We classify the Dehn functions of $M_{\Phi}$ in terms of $\Phi$ for a…

For an integer $d\ge 2$, $t\in \mathbb{R}$ and a $0$-homogeneous function $\Phi\in C^{\infty}(\mathbb{R}^{d}\setminus\{0\},\mathbb{R})$, we consider the family of Fourier multiplier operators $T_{\Phi}^t$ associated with symbols $\xi\mapsto…

We study the behaviour of functions of self-adjoint operators under relatively bounded and relatively trace class perturbation We introduce and study the class of relatively operator Lipschitz functions. An essential role is played by…

We define two types of the $\alpha$-Farey maps $F_{\alpha}$ and $F_{\alpha, \flat}$ for $0 < \alpha < \tfrac{1}{2}$, which were previously defined only for $\tfrac{1}{2} \le \alpha \le 1$ by R.~Natsui (2004). Then, for each $0 < \alpha <…

Two bounded linear operators $A$ and $B$ are parallel with respect to a norm $\|\cdot\|$ if $\|A+\mu B\| = \|A\| + \|B\|$ for some scalar $\mu$ with $|\mu| = 1$. Characterization is obtained for bijective linear maps sending parallel…

Let $\phi$ be a positive unital normal map of a von Neumann algebra $M$ into itself, and assume there is a family of normal $\phi$-invariant states which is faithful on the von Neumann algebra generated by the image of $\phi$. It is shown…

We introduce a property of a matrix-valued linear map $\Phi$ that we call its "non-m-positive dimension" (or "non-mP dimension" for short), which measures how large a subspace can be if every quantum state supported on the subspace is…

We show that each positive map from B(K) to B(H) with K and H finite dimensional Hilbert spaces is a scalar multiple of a map of the form $Tr - \psi$ with $\psi$ completely positive. This is used to give necessary and sufficient conditions…

Real and complex norms of a linear operator acting on a normed complexified space are considered. Bounds on the ratio of these norms are given. The real and complex norms are shown to coincide for four classes of operators: 1) real linear…

In this paper we present a class of maps for which the multiplicativity of the maximal output p-norm holds when p is 2 and p is larger than or equal to 4. The class includes all positive trace-preserving maps from the matrix algebra on the…

A $\mathbb{T}$-gain graph, $\Phi = (G, \varphi)$, is a graph in which the function $\varphi$ assigns a unit complex number to each orientation of an edge, and its inverse is assigned to the opposite orientation. The associated adjacency…

Suppose that $S_1$ and $S_2$ are nonempty subsets of a complete metric space $(\mathcal{M},d)$ and $\phi,\psi:S_1\to S_2$ are mappings. The aim of this work is to investigate some conditions on $\phi$ and $\psi$ such that the two functions,…

Arveson's extension theorem guarantees that every completely positive map defined on an operator system can be extended to a completely positive map defined on the whole C*-algebra containing it. An analogous statement where complete…

Let $\mathbb{B}_J(\mathcal H)$ denote the set of self-adjoint operators acting on a Hilbert space $\mathcal{H}$ with spectra contained in an open interval $J$. A map $\Phi\colon\mathbb{B}_J(\mathcal H)\to {\mathbb B}(\mathcal H)_\text{sa} $…

Two proper polynomial maps $f_1, \,f_2 \colon \mC^n \lr \mC^n$ are said to be \emph{equivalent} if there exist $\Phi_1,\, \Phi_2 \in \textrm{Aut}(\mC^n)$ such that $f_2=\Phi_2 \circ f_1 \circ \Phi_1$. In this article we investigate proper…

We derive the sharp vectorial Kato inequality for $p$-harmonic mappings. Surprisingly, the optimal constant differs from the one obtained for scalar valued $p$-harmonic functions by Chang, Chen, and Wei. As an application we demonstrate how…

In this paper, we consider the class of generalized {\Phi}-strongly monotone mappings and the methods of approximating a solution of equations of Hammerstein type. Auxiliary mapping is defined for nonlinear integral equations of Hammerstein…