共查询到20条相似文献,搜索用时 15 毫秒
1.
Lin Huaxin 《数学年刊B辑(英文版)》1993,14(3):387-396
The author studies the problem whether a multiplier of a hereditary C^*-subalgebra B of a C^*-algebra A can be extended to a multiplier of A. One related problem is the Hahn-Banach extension theorem for Hilbert modules over C^*-algebras. It is shown that every self-dual Hilbert module over W^*-algebra or an injective C^*-algebra is injective. 相似文献
2.
The authors prove that the crossed product of an infinite dimensional simple separable unital C*-algebra with stable rank one by an action of a finite group with the tracial Rokhlin property has again stable rank one. It is also proved that the crossed product of an infinite dimensional simple separable unital C*-algebra with real rank zero by an action of a finite group with the tracial Rokhlin property has again real rank zero. 相似文献
3.
本文研究Pontrjagin空间上一般算子代数弱闭和一致闭的等价条件,得到定理:设C0(U),C1(U,L,R,D,V),C2a(U),C2b(U,R),C3a(U),C3b(U,R)分别是Ⅱk空间上第0,Ⅰ,Ⅱa,Ⅱb,Ⅲa和Ⅲb类的算子代数,则(1)C0(U),C2a(U)或C3a(U)为一致闭(弱闭)的等价条件是U是Hibert空间G上的C*-代数(W*-代数;(2)C1(U,L,R,D,V)为一致闭(弱闭)的等价条件是U是Hibert空间H上的C*-代数(W*-代数),并且R是闭子空间,V是闭算子,L对称闭的;(3)C2b(U,R)或C3b(U,R)为一致闭(弱闭)的等价条件是U是Hibert空间H上的C*-代数(W*-代数),并且R是闭子空间. 相似文献
4.
Order unit property of a positive element in aC* -algebra is defined. It is proved that precisely projections satisfy this order theoretic property. This way, unital hereditary
C*-subalgebras of aC* -algebra are characterized. 相似文献
5.
George A. Elliott Katsunori Kawamura 《Transactions of the American Mathematical Society》2008,360(9):4841-4862
The category of Hilbert C*-modules over a given C*-algebra is shown to be equivalent to a certain simply described category of Hilbert bundles (i.e., continuous fields of Hilbert spaces) over the space of pure states of the C*-algebra with the zero functional adjoined.
6.
本文证明了:如果两个W~*-三元算子环V和W的cb距离d_(cb)(V,W)很小的时候,其连接冯·诺依曼代数之间的距离也很小.还证明了:和内射的W~*-三元算子环靠的很近的W~*-三元算子环也是内射的.对具有r性质和McDuff性质的W~*-三元算子环,类似的结论也成立. 相似文献
7.
本文指出,交换的(复)W 代数的大部分结果对于实情形仍然成立,自然有周期为2同胚的差别.此外,不同于复情形,可分实Hilbert空间中不包含任何极小投影的交换实VN代数同构于L∞([0,1]),L∞r([0,1])或L∞([0,1])L∞r([0,1]). 相似文献
8.
9.
Sun Huarong 《数学年刊B辑(英文版)》1992,13(4):463-470
This paper discusses the ideal structure in tensor product $A\bigotimes B$ of C^*-algebra A and B,and introduces the concept of property (I) and property (K) with respect to the problem.When A is an AF(or scattered) C^*-algebra,it is shown that for any C^*-algebra B,the ideals in $A\bigotimes B$ can be expressed by those of A and B. 相似文献
10.
本文引入了一类迹稳定秩一的C*-代数,证明了迹稳定秩一的C*-代数与AF-代数的张量积是迹稳定秩一的,得到了一个可分的单的有单位元的迹稳定秩一的,并且具有SP性质的C*-代数是稳定秩一的.同时,还讨论了迹稳定秩一的C*-代数的K-群的某些性质. 相似文献
11.
12.
本文指出:如果有两个*运算使得同一个实Banach代数均成为实C*-代数,则这两个*运算必然是相同的,即实C*-代数中*运算是唯一的. 相似文献
13.
本文给出了有限维实C~*-代数复化中标准矩阵单位基的描述,继而给出了(AF)实C~*-代数的等价定义. 相似文献
14.
证明了一类C~*-代数的弱无孔性质可以遗传到通过此类C~*-代数迹逼近后得到的C~*-代数中.同时证明了具有弱无孔性质的C~*-代数经过具有迹Rokhlin性质的有限群作用后得到的交叉积C~*-代数也具有弱无孔性质。 相似文献
15.
《数学年刊B辑(英文版)》2016,(3)
Extending the notion of Haagerup property for finite von Neumann algebras to the general von Neumann algebras, the authors define and study the(**)-Haagerup property for C*-algebras in this paper. They first give an answer to Suzuki's question(2013), and then obtain several results of(**)-Haagerup property parallel to those of Haagerup property for C*-algebras. It is proved that a nuclear unital C*-algebra with a faithful tracial state always has the(**)-Haagerup property. Some heredity results concerning the(**)-Haagerup property are also proved. 相似文献
16.
We show that a C*-algebra is a 1-separably injective Banach space if and only if it is linearly isometric to the Banach space \({C_0(\Omega)}\) of complex continuous functions vanishing at infinity on a substonean locally compact Hausdorff space \({\Omega}\). 相似文献
17.
Emmanuel Breuillard Mehrdad Kalantar Matthew Kennedy Narutaka Ozawa 《Publications Mathématiques de L'IHéS》2017,126(1):35-71
A discrete group is said to be C*-simple if its reduced C*-algebra is simple, and is said to have the unique trace property if its reduced C*-algebra has a unique tracial state. A dynamical characterization of C*-simplicity was recently obtained by the second and third named authors. In this paper, we introduce new methods for working with group and crossed product C*-algebras that allow us to take the study of C*-simplicity a step further, and in addition to settle the longstanding open problem of characterizing groups with the unique trace property. We give a new and self-contained proof of the aforementioned characterization of C*-simplicity. This yields a new characterization of C*-simplicity in terms of the weak containment of quasi-regular representations. We introduce a convenient algebraic condition that implies C*-simplicity, and show that this condition is satisfied by a vast class of groups, encompassing virtually all previously known examples as well as many new ones. We also settle a question of Skandalis and de la Harpe on the simplicity of reduced crossed products. Finally, we introduce a new property for discrete groups that is closely related to C*-simplicity, and use it to prove a broad generalization of a theorem of Zimmer, originally conjectured by Connes and Sullivan, about amenable actions. 相似文献
18.
Unbounded C*-seminorms generated by families of biweights on a partial *-algebra are considered and the admissibility of biweights
is characterized in terms of unbounded C*-seminorms they generate. Furthermore, it is shown that, under suitable assumptions,
when the family of biweights consists of all those ones which are relatively bounded with respect to a given C*-seminorm q, it can be obtained an expression for q analogous to that one which holds true for the norm of a C*-algebra. 相似文献
19.
N. T. Nemesh 《Functional Analysis and Its Applications》2016,50(2):157-159
A criterion for the topological injectivity of an AW*-algebra as a right Banach module over itself is given. A necessary condition for a C* -algebra to be topologically injective is obtained. 相似文献
20.
We prove that a number of classes of separable unital C*-algebras are closed under crossed products by finite group actions with the Rokhlin property, including: (a) AI algebras, AT algebras, and related classes characterized by direct limit decompositions using semiprojective building blocks. (b) Simple unital AH algebras with slow dimension growth and real rank zero. (c) C*-algebras with real rank zero or stable rank one. (d) Simple C*-algebras for which the order on projections is determined by traces. (e) C*-algebras whose quotients all satisfy the Universal Coefficient Theorem. (f) C*-algebras with a unique tracial state. Along the way, we give a systematic treatment of the derivation of direct limit decompositions from local approximation conditions by homomorphic images which are not necessarily injective. 相似文献