On Young and Heinz inequalities for τ-measurable operators

The purpose of this article is to prove Young and Heinz inequalities for τ-measurable operators.     

On the equations defining monomial curves

Let C be a monomial curve in three dimensional projective space over an algebraically closed field K of characteristic zero . We give several necessary criterions for C to be set theoretic complete intersection. Using these criterions we get several restrictions concerning the form of the equations that define C set theoretically.     

Tracial algebras and an embedding theorem

We prove that every positive trace on a countably generated ∗-algebra can be approximated by positive traces on algebras of generic matrices. This implies that every countably generated tracial ∗-algebra can be embedded into a metric ultraproduct of generic matrix algebras. As a particular consequence, every finite von Neumann algebra with separable pre-dual can be embedded into an ultraproduct of tracial ∗-algebras, which as ∗-algebras embed into a matrix-ring over a commutative algebra.     

A semi-finite algebra associated to a subfactor planar algebra

We canonically associate to any planar algebra two type II_∞ factors M_±. The subfactors constructed previously by the authors in Guionnet et al. (2010) [6] are isomorphic to compressions of M_± to finite projections. We show that each M_± is isomorphic to an amalgamated free product of type I von Neumann algebras with amalgamation over a fixed discrete type I von Neumann subalgebra. In the finite-depth case, existing results in the literature imply that M₊≅M₋ is the amplification a free group factor on a finite number of generators. As an application, we show that the factors Mj constructed in Guionnet et al. (in press) [6] are isomorphic to interpolated free group factors L(F(rj)), rj=1+2δ−2j(δ−1)I, where δ² is the index of the planar algebra and I is its global index. Other applications include computations of laws of Jones-Wenzl projections.     

带Neumann边值条件的非线性微分算子逆的正性

本文研究一类带Neumann边值条件的非线性微分算子.利用Wirtinger不等式,比较定理,最大值原理以及上下解方法得到了该算子的双射性和逆算子的正性结论.     

Von Neumann equivalence and group exactness

We will show that group exactness is a von Neumann equivalence invariant. This result generalizes the previously known fact stating that group exactness is stable under measure equivalence and W*-equivalence.     

Von Neumann代数上P点ξ-Lie导子的刻画

设A是没有I_1型中心直和项的von Neumann代数,P∈A是一个非中心的空核投影且其中心包络是I.研究了Von Neumann代数上P点ξ-Lie导子δ,得到了对任意A∈A,存在T∈A使得δ(A)=AT-TA,这里非零数ξ∈F且ξ≠±1.     

The Birman-Schwinger principle in von Neumann algebras of finite type

We introduce a relative index for a pair of dissipative operators in a von Neumann algebra of finite type and prove an analog of the Birman-Schwinger principle in this setting. As an application of this result, revisiting the Birman-Krein formula in the abstract scattering theory, we represent the de la Harpe-Skandalis determinant of the characteristic function of dissipative operators in the algebra in terms of the relative index.     

Perturbations of certain crossed product algebras by free groups

Given two von Neumann algebras M and N   acting on the same Hilbert space, d(M,N)$d(M,N)$ is defined to be the Hausdorff distance between their unit balls. The Kadison–Kastler problem asks whether two sufficiently close von Neumann algebras are spatially isomorphic. In this article, we show that if _P0$P_0$ is an injective von Neumann algebra with a cyclic tracial vector, G is a free group, α is a free action of G   on _P0$P_0$ and N   is a von Neumann algebra such that d(N,_P0?αG)<1/7×10⁻⁷$d(N,P_0{?}_{\alpha }G)<1/7\times {10}^{-7}$, then N   and _P0?αG$P_0{?}_{\alpha }G$ are spatially isomorphic. Suitable choices of the actions give the first examples of infinite noninjective factors for which this problem has a positive solution.     

The classification problem for von Neumann factors

We prove that it is not possible to classify separable von Neumann factors of types II₁, II_∞ or IIIλ, 0?λ?1, up to isomorphism by a Borel measurable assignment of “countable structures” as invariants. In particular the isomorphism relation of type II₁ factors is not smooth. We also prove that the isomorphism relation for von Neumann II₁ factors is analytic, but is not Borel.     

正则环与YJ-内射性

文献 [1]中 ,Ming.R.Y.C引进了 YJ 内射模的概念 ,且指出正则环上的每个模均是 YJ 内射模 ,那么反之如何呢 ?文 [1]中做了一些结果 ,本文拟就这个问题作进一步讨论 .     

COMMUTATIVE RINGS WITH FINITE QUOTIENT FIELDS

Abstract

We consider the class of all commutative reduced rings for which there exists a finite subset T ? A such that all projections on quotients by prime ideals of A are surjective when restricted to T. A complete structure theorem is given for this class of rings,and it is studied its relation with other finiteness conditions on the quotients of a ring over its prime ideals.     

Condensation of Least-energy Solutions of a Semilinear Neumann Problem

This paper is devoted to the study of tho least-energy solutions of a singularly perturbed Neumann problem involving critical Sobolev exponents. The condensation rate is given when n > 4 apd an asymptotic behavior result is obtained.     

On the double commutant of Cowen-Douglas operators

Let T be a Cowen-Douglas operator. In this paper, we study the von Neumann algebra V^?(T) consisting of operators commuting with both T and T^? from a geometric viewpoint. We identify operators in V^?(T) with connection-preserving bundle maps on E(T), the holomorphic Hermitian vector bundle associated to T. By studying such bundle maps, the structure of V^?(T) as well as information on reducing subspaces of T can be determined.     

Boundary integral equations with the generalized Neumann kernel for Laplace’s equation in multiply connected regions

This paper presents a new boundary integral method for the solution of Laplace’s equation on both bounded and unbounded multiply connected regions, with either the Dirichlet boundary condition or the Neumann boundary condition. The method is based on two uniquely solvable Fredholm integral equations of the second kind with the generalized Neumann kernel. Numerical results are presented to illustrate the efficiency of the proposed method.