算子值酉随机矩阵及其渐近自由性

该文在算子值非交换概率空间上引入半标准酉随机矩阵的概念, 证明了它是算子值Haar酉元的矩阵模型,并给出了半标准酉随机矩阵的渐近自由判定定理.     

超空间上的选择算子理论与集值随机过程

本文首次引入了超空间(子集空间)上选择算子概念,给出了几类选择算子的存在定理。作为它们的应用,给出了集值随机变量同分布的选择刻画;圆满解决了依分布收敛集值随机变量列的向量值选择问题;研究了集值随机过程的正则选择与Markov选择,给出了集值Markov过程的离散化定理,证明了紧凸集值渐近鞅的向量值渐近鞅选择存在定理。     

无界分块算子矩阵的谱分布

本文首先给出次对角元有界的2×2阶无界算子矩阵的Gershgorin定理,然后利用主对角元算子的谱和数值域刻画整个算子矩阵的谱分布.特别地,当次对角元算子互为共轭(反共轭)算子时,结合二次数值域和Gershgorin定理对谱分布给出更精细的描述.     

一类多值算子方程的迭代算法

本讨论Hilbert空间上具有强单调、上半Lipschitz连续性质的多值算子方程的求解方法,构造了迭代格式并证明迭代过程是收敛的;同时给出它在求解多值微分方程边值问题中的应用。     

算子值函数的稳定收敛性

本文给出了算子值函数稳定收敛性的一个等价条件;特别地,讨论了符号在C(S~n)+H~∞(S~n)中的 Toeplitz 算子的稳定收敛性.     

2 × 2 算子矩阵的正性*

本文主要研究 2 × 2 算子矩阵的正性,并利用极大Tseng逆理论等给出了 2 × 2 算子矩阵为正算子的等价条件.此外, 给出一类正算子矩阵的平方根算子表达式.     

一类抽象动力算子的谱

本文提出了一类新的抽象动力算子,研究了这类算子的本质谱及离散本征值的分布。作为应用,本文给出了带有周期边界条件的具各向异性散射的迁移算子的谱分析。     

一类广义区间值模糊粗糙集的公理化刻画

首先在一般区间值模糊关系上定义了两个论域上的一类广义区间值模糊粗糙集.借助区间值模糊集的截集给出区间值模糊粗糙上、下近似算子的一般表示.讨论了各种特殊的区间值模糊关系与区间值模糊近似算子性质之间的等价刻画.最后利用公理化方法刻画区间值模糊粗糙集.描述区间值模糊上、下近似算子的公理集保证了生成相同近似算子的区间值模糊关系的存在性.     

随机收缩与随机集值算子方程解集的稳定性

本文应用随机收缩,建立具有随机定义域的随机集值算子方程随机解集的稳定性定理,其推论给出了随机集值算子随机不动点集的稳定性。     

带有Radon-Nikodym导数的算子值自由Fisher信息量

本文研究了带有Radon-Nikodym导数的算子值自由Fisher信息量.利用模框架理论,得到了一个半圆元和一个子代数之间的合并自由关系,推广了D.Voiculescu等人的工作.     

自由Fisher信息量与合并自由

在算子值非交换概率空间中引入算子值自由Fisher信息量的概念,这一定义是对D.Voiculescu在有迹的von Neumann代数上定义的自由Fisher信息量的推广．证明了算子值自由Fisher信息量与合并自由性是密切相关的,即证明了若干个算子值随机变量的自由Fisher信息量的可加性等价于这些随机变量的合并自由性．并且也类似地得到了Cramer-Rao不等式．     

On Operator-Valued Semicircular Random Variables

In this paper, we discuss some special properties of operator-valued semicircular random variables including representation of the Cauchy transform of a compactly supported probability measure in terms of their operator-valued Cauchy transforms and existence of nonzero discrete part of their associated distributions.     

算子值条件自由随机变量

本文把R．Speicher的条件自由的概念推广到算子值非交换概率空间中,并利用累积函数给出一个等价定义,进而很容易地得到满足条件自由的随机变量的Voiculescu加法卷积公式．     

DIFFERENTIAL INEQUALITIES OF OPERATOR-VALUED ANALYTIC FUNCTIONS

1 IntroductionLet H dellote a colllplex Hilbert space. Let B(H) be a co1llplex Banach space of all boundedliuear operators on H, alld B(H)*, tl1e co11jugate space of B(H). The real and inlaginary partsrof all operator T on H are denoted by ReT and IlllT, respectively, i.e., ReT = op, I111T =ng. A contraction is a11 operator T E B(H) with 11TI1 5 1, a proper contractioll is al1operator T 6 B(H) witl1 lITlI < 1.We say that f is all operator-val[1ed fullction on the u1lit disc A = {…     

GENERALIZED OPERATORS AND OPERATOR-VALUED DISTRIBUTIONS IN QUANTUM FIELD THEORY

The relation between generalized operators and operator-valued distributions is discussed so that these two viewpoints can be used alternatively to explain quantum fields.     

Integral operators with operator-valued kernels

Under fairly mild measurability and integrability conditions on operator-valued kernels, boundedness results for integral operators on Bochner spaces L_p(X) are given. In particular, these results are applied to convolutions operators.     

On operator-valued Fourier multipliers

We give a simpler proof of a result on operator-valued Fourier multipliers on Lp([0,2π]d;X) using an induction argument based on a known result when d=1.     

A New Concept of the Analytic Operator-Valued Feynman Integral on Wiener Space

In this article we introduce a new concept of an analytic operator-valued Feynman integral for functionals on Wiener space, which we then use to explain various physical phenomena. We then establish the existence of some analytic operator-valued Feynman integrals that prove useful in establishing various applications in quantum mechanics.     

Statistical decision theory for quantum systems

Quantum statistical decision theory arises in connection with applied problems of optimal detection and processing of quantum signals. In this paper we give a systematic treatment of this theory, based on operator-valued measures. We study the existence problem for optimal measurements and give sufficient and necessary conditions for optimality. The notion of the maximum likelihood measurement is introduced and investigated. The general theory is then applied to the case of Gaussian (quasifree) states of Bose systems, for which optimal measurements of the mean value are found.