矩阵组的联合数值半径的次微分集

n-元算子不等式的新集合

A new collection of $n-$tuple operator inequalities

本文提出了一种新的n-元算子不等式集合，通过比较现有文献中的界，展示了其在三角不等式、算子矩阵数值半径及奇异值界方面的独特贡献。

Euclidean 算子半径的估计

Estimations of Euclidean operator radius

本文利用 2×2 分块矩阵正性判据与极分解，给出 d 元组算子乘积及 n×n 算子矩阵 Euclidean 算子半径的若干新上界。

关于算子元组的谱半径

On the spectral radius of operator tuples

本文研究了算子空间结构对算子元组谱半径的影响，证明了谱半径仅依赖于底层规范空间，并探讨了不同结构下谱半径的差异及等价条件。

联合$(f,δ)$-数值半径函数的下界和上界

Lower and upper bounds of joint $(f,δ)$-numerical radius functions

本文扩展了希尔伯特空间算子$n$元组的联合数值半径经典结果至联合$(f,δ)$-数值半径，提出新的估计方法，探讨了扇形算子中$(f,δ)$-数值半径的上下界。

算子空间上矩阵的谱半径

A spectral radius for matrices over an operator space

本文为算子空间结构定义谱半径函数，证明其小于1等价于矩阵元组联合相似于严格压缩，并揭示其与非交换有理函数定义域的关联。

On joint numerical radius of operators and joint numerical index of a Banach space

Generalizing the notion of numerical range and numerical radius of an operator on a Banach space, we introduce the notion of joint numerical range and joint numerical radius of tuple of operators on a Banach space. We study the convexity of the joint numerical range. We show that the joint numerical radius defines a norm if and only if the numerical radius defines a norm on the corresponding space. Then we prove that on a finite-dimensional Banach space, the joint numerical radius can be retrieved from the extreme points. Furthermore, we introduce a notion of joint numerical index of a Banach …

希尔伯特空间与半希尔伯特空间中算子的联合$q$-数值域

Joint $q$-Numerical Ranges of Operators in Hilbert and Semi-Hilbert Spaces

该研究提出并探究希尔伯特空间中有界线性算子组的$q$-数值域，建立相关$q$-数值半径不等式，还将其拓展至半希尔伯特空间并证明凸性，给出相关结果。

顺从迹与联合数值半径

Amenable traces and the joint numerical radius

本文利用单位元、等距元和部分等距元的联合自由数值半径，给出了C*-代数上存在顺从迹的充要刻画，并应用于获得各种提升性质的新障碍。

精细化的数值半径估计与欧几里得算子半径

Refined numerical radius estimates and Euclidean operator radius

本文通过细化方法获得算子数值半径的新估计，并利用欧几里得算子半径改进了交换子的数值半径不等式。

Hyperbolic geometry on noncommutative balls

In this paper, we study the hyperbolic geometry of noncommutative balls generated by the joint operator radius $ω_ρ$, $ρ\in (0,\infty]$, for $n$-tuples of bounded linear operators on a Hilbert space. In particular, $ω_1$ is the operator norm, $ω_2$ is the joint numerical radius, and $ω_\infty$ is the joint spectral radius. We provide mapping theorems, von Neumann inequalities, and Schwarz type lemmas for free holomorphic functions on noncommutative balls, with respect to the hyperbolic metric $δ_ρ$, the Carath\' eodory metric $d_K$, and the joint operator radius $ω_ρ$.

Unitary invariants in multivariable operator theory

The problems considered in this paper come as a natural continuation of our program to develop a free analogue of Sz.-Nagy-Foias theory, for row contractions. The paper is structured as follows: Introduction Part I. Unitary invariants for n-tuples of operators 1. Joint numerical radius 2. Euclidean operator radius 3. Joint numerical range and spectrum 4. $ρ$-operator radius Part II. Joint operator radii, inequalities, and applications 5. von Neumann inequalities 6. Constrained von Neumann inequalities 7. Multivariable Haagerup-de la Harpe inequalities 8. Multivariable Fejer inequalities Refere…

Spectral sets and operator radii

We study different operator radii of homomorphisms from an operator algebra into $B(H)$ and show that these can be computed explicitly in terms of the usual norm. As an application, we show that if $Ω$ is a $K$-spectral set for a Hilbert space operator, then it is a $M$-numerical radius set, where $M=\frac{1}{2}(K+K^{-1})$. This is a counterpart of a recent result of Davidson, Paulsen and Woerdeman. More general results for operator radii associated with the class of operators having $ρ$-dilations in the sense of Sz.-Nagy and Foias are given. A version of a result of Drury concerning the joint…

广义球面Aluthge变换的谱图与联合谱半径

The Spectral Picture and Joint Spectral Radius of the Generalized Spherical Aluthge Transform

本文研究了广义球面Aluthge变换的谱图，并证明了通过该变换的迭代范数可计算原算子的谱半径。