算子的ω-非负逼近

<正> 文中 H 为可析 Hilbert 空间,H 中内积为〈·,·〉,H 中向量的范数为‖·‖,(?)(H)为H 上线性有界算子全体,对任何 T∈(?)(H),‖T‖表示算子 T 的范数.记     

算子的最佳非负逼近

<正> 在本文中 H 表示完备内积空间,〈·,·〉表示 H 中元对的内积.(H,H)表示定义在H 上取值于 H 的有界线性算子组成的 Banach 空间,本文中的算子都是 (H,H) 中的元.若自伴算子 P∈(H,H),〈Px,x〉≥0 (?)x∈H,则称 P 是非负算子,记作 P≥0.A∈(H,H),定义δ(A)=(?){‖A—P‖},其中‖·‖表示 (H,H) 中元的范数.若 P_0≥0,P_0∈(H,H) 使δ(A)=(?){‖A—P‖}=‖A—P_0‖,则称 P_0是 A 的最佳非负逼近.研究     

强K(a)hler-Finsler流形上(p,q)形式的中值Laplace算子

本文给出了强K(a)hler-Finsler流形上中值Laplace算子的一些性质,如自伴性质,散度形式等.与K(a)hler流形上利用逆变基本张量[11]及其在Finsler流形上的变形[5,10]作为密度函数定义流形上的逐点内积及整体内积不同,作者利用强K(a)hler-Finsler流形上的逆变密切Kahler度量作为密度函数定义了流形上的逐点内积和整体内积,并定义了强K(a)hler-Finsler流形上的Hodge-Laplace算子,它可看作函数情形中值Laplace算子的推广.     

强Khler-Finsler流形上(p,q)形式的中值Laplace算子(英文)

本文给出了强Khler-Finsler流形上中值Laplace算子的一些性质,如自伴性质,散度形式等。与Khler流形上利用逆变基本张量及其在Finsler流形上的变形作为密度函数定义流形上的逐点内积及整体内积不同,作者利用强Khler-Finsler流形上的逆变密切Khler度量作为密度函数定义了流形上的逐点内积和整体内积,并定义了强Khler-Finsler流形上的Hodge-Laplace算子,它可看作函数情形中值Laplace算子的推广。     

Hilbert空间中线性系统的一个镇定问题

<正> 本文考察复 Hilbert 空间(?)中的线性系统(?)(1)在反馈律Gu(t)=-sum from i=1 to v b_i〈(dy)/(dt),g_i〉 (2)下的镇定问题,其中〈·,·〉表(?)中内积,d·/dt 表矢值函数“·”的微商,u(t)为数值函数.假设:(A)算子 A 为正定自伴离散谱算子,谱分解式为     

强Kaehler-Finsler流形上（p，q）形式的中值Laplace算子

本文给出了强Kaehler-Finsler流形上中值Laplace算子的一些性质，如自伴性质，散度形式等。与Kaehler流形上利用逆变基本张量及其在Finsler流形上的变形作为密度函数定义流形上的逐点内积及整体内积不同，作者利用强Kaehler-Finsler流形上的逆变密切Kaehler度量作为密度函数定义了流形上的逐点内积和整体内积，并定义了强Kaehler-Finsler流形上的Hodge-Laplace算子，它可看作函数情形中值Laplace算子的推广。     

密度矩阵的表示

介绍了密度矩阵的概念、Hilbert-Schmidt内积、由此内积诱导的范数,然后以矩阵及算子理论为基础,借助内积这一数学工具给出了二阶、四阶、八阶密度阵的表示,并对二阶、四阶、八阶密度阵表示进行了分析,得到了相关结论,最后将其结论推广到2~n阶密度阵.     

Levy-Meixner场的交互作用Fock表示及量子Levy-Meixner过程

本文利用Gamma分布的n阶矩与半不变量之间的组合关系,在Fock空间的一个稠子空间上定义了一个新的内积,按此内积完备化得到交互作用Fock空间.在此交互作用Fock空间上重新定义了增生,保守,湮灭算子.最后考虑了由三种算子的线性组合所构成的量子Levy-Meixner过程.     

连续切波变换反演公式的级数表示

我们主要研究连续切波变换反演公式的级数表示.首先引入两类由切波变换反演公式定义的无穷级数和有限级数,并研究了由Kittipoom等人介绍的切波生成空间,得到这个切波生成空间的一些重要性质.其次利用这些结果显示:对于这个切波生成空间,当采样密度趋于无穷时由我们定义的无穷级数按L~2-范数收敛于重构函数;对于可允许函数空间,当采样密度趋于无穷时由我们定义的有限级数按L~2-范数收敛于重构函数.     

球几何迁移算子的豫解算子的非全连续性

雷勒(J.Lehner)在[1]中说到:在希尔柏特空间H中球几何迁移算子A的豫解算子是全连续算子,这个结论是不正确的,下面给出证明:设希尔柏特空间H是图中的半圆上以P(x,y)=y为权的绝对平方可积函数的空间,内积定义为其中。线性算子A定义如下:的定义域为关于x绝对连续,其中是大于零的常数,     

An inner product lemma

Given the operator product BA in which both A and B are symmetric positive‐definite operators, for which symmetric positive‐definite operators C is BA symmetric positive‐definite in the C inner product 〈x, y〉C? This question arises naturally in preconditioned iterative solution methods, and will be answered completely here. Copyright © 2004 John Wiley & Sons, Ltd.     

Invariant subspaces of positive strictly singular operators on Banach lattices

It is shown that every positive strictly singular operator T on a Banach lattice satisfying certain conditions is AM-compact and has invariant subspaces. Moreover, every positive operator commuting with T has an invariant subspace. It is also proved that on such spaces the product of a disjointly strictly singular and a regular AM-compact operator is strictly singular. Finally, we prove that on these spaces the known invariant subspace results for compact-friendly operators can be extended to strictly singular-friendly operators.     

多线性分数次积分算子一般框架下的交换子的有界性——献给陆善镇教授75华诞

对任意给定的正整数m,Z^＋×{1,...,m}的任意一个有限子集S,定义一般化的多线性分数次积分算子的交换子Iα,→b,S（f）（x）=∫（Rn）^m ∏（i,j）∈S（bi（x）-bi（yj））/（｜x-y1｜＋…＋｜x-ym｜）^mn-α∏（j=1→m）fj（yj）d→y,其中d→y=dy1…dym.此框架下的交换子包含了以往研究的各类分数次积分算子的交换子,并蕴含了多线性背景下新的交换子形式.在上述非常一般框架下,本文给出带多重A→p,q权的多线性分数次积分算子的交换子Iα,→b,S（→f）的加权强型（L^p1（ω1）×···×L^pm（ωm）,L^q（ν→ωq））估计和加权弱型端点估计.本文还得到更一般核条件下的上述结果.     

Bernstein-Type Operators on the Half Line

We define Bernstein-type operators on the half line [0, +[ by means of two sequences of strictly positive real numbers. After studying their approximation properties, we also establish a Voronovskaja-type result with respect to a suitable weighted norm.     

τ-可测正算子生成的交换子的若干不等式

设M是具有正规忠实的半有限迹τ的von Neumann代数,‖.‖ρ是任意非交换Banach函数空间范数,‖.‖是M上的通常范数.证明了若A和B是τ-可测正算子,X∈M,则‖AX-XB‖ρ≤‖X‖‖AB‖ρ.还证明了若A,B是M中的正算子,X是τ-可测算子,则‖AX-XB‖ρ≤max(‖A‖,‖B‖)‖X‖ρ.由此得到了若A∈M是正算子,X是τ-可测正算子,则‖AX-XA‖ρ≤1/2‖A‖‖XX‖ρ.     

Non-Archimedean Analogues of Orthogonal and Symmetric Operators and p-adic Quantization

We study orthogonal and symmetric operators in non-Archimedean Hilbert spaces in the connection with p-adic quantization. This quantization describes measurements with finite precision. Symmetric (bounded) operators in the p-adic Hilbert spaces represent physical observables. We study spectral properties of one of the most important quantum operators, namely, the operator of the position (which is represented in the p-adic Hilbert L₂-space with respect to the p-adic Gaussian measure). Orthogonal isometric isomorphisms of p-adic Hilbert spaces preserve precisions of measurements. We study properties of orthogonal operators. It is proved that each orthogonal operator in the non-Archimedean Hilbert space is continuous. However, there exist discontinuous operators with the dense domain of definition which preserve the inner product. There also exist nonisometric orthogonal operators. We describe some classes of orthogonal isometric operators and we study some general questions of the theory of non-Archimedean Hilbert spaces (in particular, general connections between topology, norm and inner product).     

Sharp bounds for multilinear fractional integral operators on Morrey type spaces

A multi-Morrey norm which is strictly smaller than m-fold product of the Morrey norms is introduced and the boundedness property of the Adams type for multilinear fractional integral operators is obtained. The optimality of the results is also discussed.     

一类积分方程的正解的存在性与可积性

讨论了与加权Hardy-Littlewood-Sobolev不等式有密切联系的一类积分方程：（？）证明了此类积分方程在L~（n（p-1）/（n-λ-β））（R~n）∩L~（q0）（R~n）中存在唯一的正解,并利用迭代技巧得到了正解的可积区间L~5（R~n）,s∈[min{qo,n（p-1）/（n-λ-β）},∞].     

Invariant sublattices for positive operators

There are, by now, many results which guarantee that positive operators on Banach lattices have non-trivial closed invariant sublattices. In particular, this is true for every positive compact operator. Apart from some results of a general nature, in this paper we present several examples of positive operators on Banach lattices which do not have non-trivial closed invariant sublattices. These examples include both AM-spaces and Banach lattices with an order continuous norm and which are and are not atomic. In all these cases we can ensure that the operators do possess non-trivial closed invariant subspaces.     

The normed finiteness property of compact contraction operators

We study the joint spectral radius given by a finite set of compact operators on a Hilbert space. It is shown that the normed finiteness property holds in this case, that is, if all the compact operators are contractions and the joint spectral radius is equal to 1 then there exists a finite product that has a spectral radius equal to 1. We prove an additional statement in that the requirement that the joint spectral radius be equal to 1 can be relaxed to the asking that the maximum norm of finite products of a length norm is equal to 1. The length of this product is related to the dimension of the subspace on which the set of operators is norm preserving.