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1.
利用 von Neumann 代数 M 和带有正规的2- 上循环 μ 的离散群 G, 定义了2- 上循环交叉积, 推广了经典的离散交叉积, 并证明了2- 上循环交叉积具有结合律.  相似文献   

2.
Saito (Math. Proc. Camb. Phil. Soc., 117, 11–20, 1995) proved Sarason’s interpolation theorem for an analytic crossed product determined by a finite von Neumann algebra. We extend this result without the assumption that the von Neumann algebra is finite.  相似文献   

3.
We investigate crossed products of Cuntz algebras by quasi-free actions of abelian groups. We prove that our algebras are AF-embeddable when actions satisfy a certain condition. We also give a necessary and sufficient condition that our algebras become simple and purely infinite, and consequently our algebras are either purely infinite or AF-embeddable when they are simple.  相似文献   

4.
In this paper, we will estimate an upper bound for the similarity degree of the crossed product of a hyperfinite finite von Neumann algebra by weakly compact action of an infinite discrete group. We will also improve some upper bounds for similarity degrees of some finite von Neumann algebras.  相似文献   

5.
The notion of Hankel operators associated with analytic crossed products were introduced and researched in [2]. In this paper, we study the adjoint of Hankel operators and give necessary and sufficient condition that the adjoint of a Hankel operator is again a Hankel operator. This work was supported in part by a Grant-in-Aid for Scientific Research, Japan Society for the Promotion of Science.  相似文献   

6.
Nonlinear maps preserving Lie products on factor von Neumann algebras   总被引:2,自引:0,他引:2  
In this paper, we prove that every bijective map preserving Lie products from a factor von Neumann algebra into another factor von Neumann algebra is of the form Aψ(A)+ξ(A), where is an additive isomorphism or the negative of an additive anti-isomorphism and is a map with ξ(AB-BA)=0 for all .  相似文献   

7.
8.
吴文明  袁巍 《数学学报》2008,51(4):803-808
设α是可数离散群G和H的半直积G■_σH在冯·诺依曼代数M上的作用,则β_h=α_((e,h))AdU_h定义了群H在冯·诺依曼代数交叉积M■_αG上的作用β.本文证明了交叉积冯·诺依曼代数M■_α(G■_σH)与(M■_αG)■_βH是*-同构的,因此在一定条件下,冯·诺依曼代数的交叉积满足结合律.  相似文献   

9.
We consider an inclusion BM of finite von Neumann algebras satisfying BMB. A partial isometry vM is called a groupoid normalizer if vBv,vBvB. Given two such inclusions BiMi, 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 vM satisfying vBvB and vv,vvB.  相似文献   

10.
We describe the lattice of the ideals generated by projections and prove a characterization of the ideal property for ``large" classes of crossed products of commutative -algebras by discrete, amenable groups; some applications are also given. We prove that the crossed product of a -algebra with the ideal property by a group with the ideal property may fail to have the ideal property; this answers a question of Shuzhou Wang.

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