群在von Neumann代数上作用的自由和遍历性注记

本文研究了群在von Neumann代数上作用的自由性和遍历性问题.利用投影和群SL2(R)的Iwasawa分解,得到了可数离散群在交换von Neumann代数上作用的自由性的等价刻画,证明了SL2(R)在上半平面H上有理作用导出的SL2(R)在极大交换von Neumann代数A={Mf:f∈L2(H,dxdy/y2)}上的作用α是遍历的,但不是自由的.     

GP-V'-环的von Neumann正则性

本文研究了GP-V'-环的von Neumann正则性问题.利用GW-理想和W-理想的性质及方法,得到了 GP-V'-环是(强)正则环的一些条件,推广了文献[3,6]中的相关结果.     

MAPS PRESERVING STRONG SKEW LIE PRODUCT ON FACTOR VON NEUMANN ALGEBRAS

Let A be a factor von Neumann algebra and Φ be a nonlinear surjective map from A onto itself.We prove that,if Φ satisfies that Φ(A)Φ(B) - Φ(B)Φ(A)* =AB - BA* for all A,B ∈ A,then there exist a linear b...     

VON NEUMANN STABILITY ANALYSIS OF SYMPLECTIC INTEGRATORS APPLIED TO HAMILTONIAN PDEs

Symplectic integration of separable Hamiltonian ordinary and partial differential equations is discussed. A von Neumann analysis is performed to achieve general linear stability criteria for symplectic methods applied to a restricted class of Hamiltonian PDEs. In this treatment, the symplectic step is performed prior to the spatial step, as opposed to the standard approach of spatially discretising the PDE to form a system of Hamiltonian ODEs to which a symplectic integrator can be applied. In this way stability criteria are achieved by considering the spectra of linearised Hamiltonian PDEs rather than spatial step size.     

On a vector-valued integral in the “noncommutative” statistical decision theory

A generalization of a vector-valued integral arising in the noncommutative (quantum) statistical decision theory is considered.     

Groupoid normalizers of tensor products

We consider an inclusion B⊆M of finite von Neumann algebras satisfying B^′∩M⊆B. A partial isometry v∈M is called a groupoid normalizer if vBv^∗,v^∗Bv⊆B. Given two such inclusions Bi⊆Mi, i=1,2, we find approximations to the groupoid normalizers of in , from which we deduce that the von Neumann algebra generated by the groupoid normalizers of the tensor product is equal to the tensor product of the von Neumann algebras generated by the groupoid normalizers. Examples are given to show that this can fail without the hypothesis , i=1,2. We also prove a parallel result where the groupoid normalizers are replaced by the intertwiners, those partial isometries v∈M satisfying vBv^∗⊆B and v^∗v,vv^∗∈B.     

Completely positive projections on a Hilbert space

The purpose of this paper is to prove that a completely positive projection on a Hilbert space associated with a standard form of a von Neumann algebra induces the existence of a conditional expectation of the von Neumann algebra with respect to a normal state, and we consider the application to a standard form of an injective von Neumann algebra.

     

ON NEUMANN PROBLEM FOR SOMESEMILINEAR ELLIPTIC EQUATIONS INVOLVING CRITICAL SOBOLEV EXPONENTS

1IntroductionLetnbeaboundeddomaininRewithCIboundarytn23.Weconsidertheprobleminwhichp=ac,q=M,7denotestheunitoutwardnormaltoon,A>0,p20.Inthisp8Per,wesuppose(Al)a(z)eL"(n),a(z)50.(afl)op(2)EC(on),op(x)20,M==op(:).(op2)op(zo)=M,icEOf.InasmallneighborhoodUofic,thedoesnQliesononesideOfthetangentplaneOfonatic,andthe(n--l)principlecurvaturesofxo(withrespecttotheinnernormalOfon)arepositive.(gi)g(z,u)ismeasurablein2,continuousinu,sup{g(2,u)::En,0Su5an}< coforeveryfixedan>0andg(x,0)=0.(g2)!5op=0…     

Spectral averaging for trace compatible operators

In this note the notions of trace compatible operators and infinitesimal spectral flow are introduced. We define the spectral shift function as the integral of infinitesimal spectral flow. It is proved that the spectral shift function thus defined is absolutely continuous and Kreĭn's formula is established. Some examples of trace compatible affine spaces of operators are given.

     

On a property ofL p spaces on semifinite von Neumann algebras

A characterization of the traces in a broad class of weights on von Neumann algebras is obtained. A new property of the domain ideals of these traces is proved. In the semifinite case, a relation for a faithful normal trace is established. This result is new even for the algebra of all bounded operators on a Hilbert space. Applications of the main result to the structure theory of von Neumann algebras and to the Köthe duality theory for ideal spaces of Segal measurable operators are given.Translated fromMatematicheskie Zametki, Vol. 64, No. 2, pp. 185–190, August, 1998.The author wishes to express his deep gratitude to Professor A. N. Sherstnev for setting the problem and for fruitful discussions.This research was supported by the Russian Foundation for Basic Research under grant No. 95-01-00025.     

Relative matched pairs of finite groups from depth two inclusions of von Neumann algebras to quantum groupoids

In this work we give a generalization of matched pairs of (finite) groups to describe a general class of depth two inclusions of factor von Neumann algebras and the C^∗-quantum groupoids associated with, using double groupoids.     

混合von Mises 模型的参数估计

有限混合von Mises模型在天文学、生物学、地理和医药等许多领域都有重要的应用．可是,不论样本量有多大,此模型的似然函数都是无界的．因此,参数的最大似然估计(MLE)是不相合的．我们发现,与混合正态模型一样,上述困难可以通过引入关于分布浓度参数的一个惩罚函数或对参数空间添加适当的约束来克服．在此文中,我们从理论上证明了这两种方法是可行的,相应的参数估计是强相合的,且是渐近有效的．我们还通过计算机模拟来探讨这些新方法在有限样本情况下的统计性质,并与现有的矩估计作了比较．结果发现,惩罚极大似然估计在均方误差方面表现最佳．最后我们还分析了一组实际数据,以进一步介绍新的估计方法．     

POSITIVE SOLUTIONS TO SECOND-ORDER SINGULAR NEUMANN BOUNDARY VALUE PROBLEM WITH PARAMETERS IN THE BOUNDARY CONDITIONS

In this paper, we consider a class of nonlinear second-order singular Neumann boundary value problem with parameters in the boundary conditions. By the fixed point index, spectral theory of the linear operators, and lower and upper solutions method, we prove that there exists a constant λ* > 0 such that for λ∈ (0, λ * ), NBVP has at least two positive solutions; for λ = λ* , NBVP has at least one positive solution; for λ > λ* , NBVP has no solution.     

Tent spaces associated with semigroups of operators

We study tent spaces on general measure spaces (Ω,μ). We assume that there exists a semigroup of positive operators on Lp(Ω,μ) satisfying a monotone property but do not assume any geometric/metric structure on Ω. The semigroup plays the same role as integrals on cones and cubes in Euclidean spaces. We then study BMO spaces on general measure spaces and get an analogue of Fefferman's H¹-BMO duality theory. We also get a H¹-BMO duality inequality without assuming the monotone property. All the results are proved in a more general setting, namely for noncommutative Lp spaces.     

几种约束广义逆矩阵的有限算法

1引言与引理众所周知，关于非奇异方阵的正则逆的有限算法是由Faddeev大给在1949年之前提出的，这就是著名的Faddeev算法[1，P…334-336]。自从五十年代中期广义逆矩阵的研究复兴与发展以来，有不少学者提出了关于广义逆矩阵的有限算法。第一个给出关于广义逆矩     

Subadditivity Inequalities in von Neumann Algebras and Characterization of Tracial Functionals

We examine under which assumptions on a positive normal functional φ on a von Neumann algebra, and a Borel measurable function f: R ⁺ → R with f(0) = 0 the subadditivity inequality φ (f(A+B)) ≤ φ(f(A))+φ (f (B)) holds true for all positive operators A, B in . A corresponding characterization of tracial functionals among positive normal functionals on a von Neumann algebra is presented. O.E. Tikhonov - Supported by the Russian Foundation for Basic Research (grant no. 01-01-00129) and the scientific program Universities of Russia – Basic Research (grant no. UR.04.01.061).