C~* -代数上完全正映射的刻画

本文给出C* -代数之间完全正映射的刻画,证明:如果A,B是有单位元的C*-代数,则映射Φ:A→B为完全正映射当且仅当存在保单位*-同态πA:A→B(K)、等距* -同态πB:B→B(H)及有界线性算子V:H→K,使得πB(Φ(1))=V*V 且■a∈A,都有πB(Φ(a))=V*π(a)V.作为推论,得到著名的Stinespring膨胀定理.     

纯无限单的C*-代数通过某些C*-代数扩张的非稳定K-理论

设0→B■E■A→0是有单位元C~*-代数E的一个扩张,其中A是有单位元纯无限单的C~*-代数,B是E的闭理想.当B是E的本性理想并且同时是单的、可分的而且具有实秩零及性质(PC)时,证明了K_0(E)={[p]| p是E\B中的投影};当B是稳定C~*-代数时,证明了对任意紧的Hausdorff空间X,有■(C(X,E))/■_0(C(X,E))≌K_1(C(X,E)).     

C~*-代数拟对角扩张的α-比较性（英文）

设A为一个含单位元的C~*-代数,且有拟对角扩张0→I→A→πA/I→0.则A具有α-比较性,当且仅当I与A/I都具有α-比较性.     

C~*代数上保持不定正交性的线性映射

设A和B是含单位元的C~*代数,s∈A和t∈B是可逆自伴元,对任意的x∈A及z∈B,定义x~+=s~(-1)x~*s,z~+=t~(-1)z~*t。假定A是实秩零的并且Φ:A→B是有界线性满射。证明了对任意的 都成立的充要条件是Φ(1)可逆,Φ(1)~+Φ(1)=Φ(1)Φ(1)~+∈Z(B)(B的中心),并且存在从A到B上的满+同态Ψ,使得对所有的x∈A都有Φ(x)=Φ(1)Ψ(x)成立。对于一般C~*代数上保正交性的线性映射Φ,在假定Φ(1)可逆的条件下,也得到类似的结果。     

拟对角扩张的近似等距提升

设 设 设0→I→A—A/I→0为C~*-代数的短正合列且A含有单位元.如果扩张0→I→A→A/I→0为拟对角扩张,则证明对任给的A/I中正元(投影,部分等距,酉元)均有同形式的提升且提升与I中一列由投影组成的拟中心近似单位元相交换.进而证明对任给正数ε,任意A/I中的两正元(投影,部分等距,酉元)a~-和b~-,以及a~-的正元(投影,部分等距,酉元)的提升a,存在b~-的正元(投影,部分等距,酉元)的提升b,使得‖a-b‖<‖a~--b~-‖ ε.作为上述结论的应用证明了对任意的正数ε和u~-∈U(A/I)_0,存在u~-的提升u∈U(A)_0,使得cel(u)相似文献   

C*-代数交叉积上的渐近同态(英文)

林华新和松井宏树提出了可分C~*-代数上的渐近同态的概念,以及Cantor极小系统上弱逼近共轭的概念.设A为Ko群有限生成的AF代数,α,β为A上的具有Rokhlin性质的*-自同构.则α和β弱逼近共轭的充要条件是,存在两列渐近同态{φ_n}:A_α→A_β和{ψ_n}:A_β→A_α,以及两列*-自同构{Φ_n},{Ψ_n}:A→A,满足对任意的a∈A,均有lim_(n→∞)‖φ_noj_α(a)-jβoΦ_n(a)‖=0和lim_(n→∞)‖ψ_nojβ(a)-jα·Ψ_n(a)‖=0.     

迹分解秩(英文)

首先引入迹分解秩的概念,具有这个结构的稳定有限的顺从C~*-代数非常多.这个概念和Elliott的用K-理论来分类顺从C~*-代数的分类计划有重要的联系.然后研究C~*-代数扩张.设0→I→A-→A/I→0是C~*-代数的一个短正合序列,其中A有单位元.假设I有分解秩k,A/I有迹分解秩k,那么如果扩张是拟对角的,本文将证明A的迹分解秩不超过k.     

第6卷 B 辑 第1期(1985)目录和提要

c~*-代数上非单位的正线性映象李炳仁通常讨论 C~*-代数到 C~*代数的正线性映象总假定它把单位元变作单位元.本文讨论的 C~*-代数不要假定有单位元.主要结果有两个:1)如果Φ是 C~*-代数 A 到 C~*-代数 B 的正线性映象,如同 A 上的正线性泛函那样,Φ的范数有如下的表达式‖Φ‖=sup{‖Φ(a)‖|a∈A_+,‖a‖≤1}=‖Φ(v_l)‖=‖Φ(v_l~2)‖,这里{v_l}是 A 的一个逼近单位元;2)如果Φ是 C~*-代数 A 到 C~* -代数 B 的 n-正线性映象,并且     

C~*-代数的迹迹秩

引入C~*-代数迹迹秩的概念,讨论它的基本性质.另外,迹迹秩为零和迹拓扑秩为零的C~*-代数等价,同时讨论这类代数的拟对角扩张性质.设O→I→A→A/I→O是拟对角扩张的短正合列,证明如果TTR(I)≤k且TTR(A/I)=0,则TTR(A)≤k.     

C^＊—代数KK—理论中的Puppe列

在C~*-代数K-理论中,K-群的计算问题是一个基本问题,解决这一问题的一个重要途径就是建立一系列相应群的正合列。在本文中,我们考虑两个C~*-代数和映射锥的KK—群之间的关系,证明其间存在一个六项Puppe列。设A、B为分层C~*—代数,φ:A→B为分层*-同态,其映射锥记为C_φ即     

RECENT PROGRESS ON SPHERICAL HARMONIC APPROXIMATION MADE BY BNU RESEARCH GROUP ——In memory of Professor Sun Yongsheng

As early as in 1990, Professor Sun Yongsheng, suggested his students at Beijing Normal University to consider research problems on the unit sphere. Under his guidance and encouragement his students started the research on spherical harmonic analysis and approximation. In this paper, we incompletely introduce the main achievements in this area obtained by our group and relative researchers during recent 5 years （2001-2005）. The main topics are： convergence of Cesaro summability, a.e. and strong summability of Fourier-Laplace series; smoothness and K-functionals; Kolmogorov and linear widths.     

On a class of self-similar processes with stationary increments in higher order Wiener chaoses

We study a class of self-similar processes with stationary increments belonging to higher order Wiener chaoses which are similar to Hermite processes. We obtain an almost sure wavelet-like expansion of these processes. This allows us to compute the pointwise and local Hölder regularity of sample paths and to analyse their behaviour at infinity. We also provide some results on the Hausdorff dimension of the range and graphs of multidimensional anisotropic self-similar processes with stationary increments defined by multiple Wiener–Itô integrals.     

A REPRESENTATION FORMULA RELATED TO SCHR(O)DINGER OPERATORS

Schr(o)dinger operator is a central subject in the mathematical study of quantum mechanics.Consider the Schrodinger operator H = -△ V on R, where △ = d2/dx2 and the potential function V is real valued. In Fourier analysis, it is well-known that a square integrable function admits an expansion with exponentials as eigenfunctions of -△. A natural conjecture is that an L2 function admits a similar expansion in terms of "eigenfunctions" of H, a perturbation of the Laplacian (see [7], Ch. Ⅺ and the notes), under certain condition on V.     

On a class of Riemann surfaces

It is considered the class of Riemann surfaces with dimT1 = 0, where T1 is a subclass of exact harmonic forms which is one of the factors in the orthogonal decomposition of the spaceΩH of harmonic forms of the surface, namely The surfaces in the class OHD and the class of planar surfaces satisfy dimT1 = 0. A.Pfluger posed the question whether there might exist other surfaces outside those two classes. Here it is shown that in the case of finite genus g, we should look for a surface S with dimT1 = 0 among the surfaces of the form Sg\K , where Sg is a closed surface of genus g and K a compact set of positive harmonic measure with perfect components and very irregular boundary.     

Boundedness for commutators of multipliers on Hardy type spaces

In this paper, we study the commutators generalized by multipliers and a BMO function. Under some assumptions, we establish its boundedness properties from certain atomic Hardy space Hb^p（R^n） into the Lebesgue space L^p with p 〈 1.     

A unified approach to certain problems of best local approximation

In this paper we study best local quasi-rational approximation and best local approximation from finite dimensional subspaces of vectorial functions of several variables. Our approach extends and unifies several problems concerning best local multi-point approximation in different norms.     

THE 8~(th) INTERNATIONAL CONGRESS ON INDUSTRIAL AND APPLIED MATHEMATICS

<正>August 10-14,2015Beijing,ChinaThe International Congress on Industrial and Applied Mathematics(ICIAM)is the premier international congress in the field of applied mathematics held every four years under the auspices of the International Council for Industrial and Applied Mathematics.From August 10 to 14,2015,mathematicians,scientists     

Towards Excellence in Science Chinese Academy of Sciences

<正>May 26,2014,Beijing Science is a human enterprise in the pursuit of knowledge.The scientific revolution that occurred in the 17th Century initiated the advances of modern science.The scientific knowledge system created by