共查询到20条相似文献,搜索用时 62 毫秒
1.
Suppose A is a unital C*-algebra and r 1.In this paper,we define a unital C*-algebra C_(cb)*(A,r) and a completely bounded unital homomorphism α_r:A → C_(cb)*(A,r)with the property that C_(cb)*(A,r)=C*(α_r(A))and,for every unital C*-algebra B and every unital completely bounded homomorphism φ:A→ B,there is a(unique)unital *-homomorphism π:C_(cb)*(A,r)→B such thatφ=πoα_r.We prove that,if A is generated by a normal set {t_λ:λ∈Λ},then C_(cb)*(A,r)is generated by the set {α_r(t_λ):λ∈Λ}.By proving an equation of the norms of elements in a dense subset of C_(cb)*(A,r)we obtain that,if Β is a unital C*-algebra that can be embedded into A,then C_(cb)*(B,r)can be naturally embedded into C(cb)*(A,r).We give characterizations of C_(cb)*(A,r)for some special situations and we conclude that C_(cb)*(A,r)will be "nice" when dim(A)≤ 2 and "quite complicated" when dim(A)≥ 3.We give a characterization of the relation between K-groups of A and K-groups of C_(cb)*(A,r).We also define and study some analogous of C_(cb)*(A,r). 相似文献
2.
Qing Zhai FAN 《数学学报(英文版)》2020,36(3):337-362
We show that the following properties of the C^*-algebras in a class Ω are inherited by simple unital C-algebras in the class TAΩ:(1)(m,n)-decomposable,(2) weakly(m,n)-divisible,(3) weak Riesz interpolation.As an application,let A be an infinite dimensional simple unital C-algebra such that A has one of the above-listed properties.Suppose that α:G→Aut(A) is an action of a finite group G on A which has the tracial Rokhlin property.Then the crossed product C^*-algebra C^*(G,A,α) also has the property under consideration. 相似文献
3.
Murray和von Neumann在对W~*-代数进行分类工作时,主要的工具是刻画W~*-代数中的投影的性质(事实上,W~*-代数是由投影所生成的).因为一般的C~*-代数可能不包含任何非零的投影,所以不能将Murray和von Neumann的方法,直接地应用到C~*-代数上来得出分类理论.本文作者在最近的两项工作中,分别使用C~*-代数的开投影和正元来代替投影,得到两套平行的Murray-von Neumann式的分类理论.本文在简单描述了这两套分类理论之后,将会给出一个一般的分类架构,它可以用来得出好些C~*-代数的分类理论(包括我们之前的两套理论),我们也会通过它来讨论各种分类理论之间的等价性,并给出之前两套理论的细化. 相似文献
4.
Ian Putnam利用Smale空间上的渐近等价关系定义了广群C~*-代数及其典则自同构.本文在零维Smale空间的情形下,计算此类C~*-自同构的逼近熵,证明了相应C~*-动力系统关于CNT熵和逼近熵的"变分原理"成立.由此推演出此类Smale空间上的Bowen测度诱导的C~*-代数上的态是此典则自同构的唯一平衡态. 相似文献
5.
研究了多重C~*-动力系统在Hilbert C~*-模上表示的膨胀.设(A,α)是一个多重C~*-动力系统,(π,T,E)是(A,α)的行压缩协变表示,证明了存在(π,T,E)的等距膨胀(ρ,V,F). 相似文献
6.
给出C~*-代数α-比较性的等价刻画:对于单的含单位元的稳定有限的C~*-代数A而言,A具有α-比较性,当且仅当对于任意的a,b∈W(A),若α·d_r(a)d_τ(b)(_τ∈QT(A)),则a≤b在Cuntz半群W(A)中成立.利用此刻画,证明了具有α-比较性的C~*-代数一定具有弱比较性;若A具有α-比较性,其中α=m+1,则A具有正元的强迹m-比较性;对于满足Kirchberg-R?rdam条件的C~*-代数,E-稳定、严格比较、α-比较性(α=m+1)、强迹m-比较性、弱比较性以及局部弱比较性彼此等价;若α:=inf{α′∈(1,∞)|A具有α′-比较}∞,则A具有α-比较性. 相似文献
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本文分别研究了 C*-代数l上的单位左模和具有实阶零性质的CC*代数l上的单位左模的半双线性型的 Hyers-Ulam 稳定性. 相似文献
9.
Qing MENG 《Frontiers of Mathematics in China》2020,15(2):385-398
We introduce and study property T and strong property T for unital*-homomorphisms between two unital C^*-algebras.We also consider the relations between property T and invariant subspaces for some canonical unital^-representations.As a corollary,we show that when G is a discrete group,G is finite if and only if G is amenable and the inclusion map i:Cr^*(G)→B(l^2(G))has property T.We also give some new equivalent forms of property T for countable discrete groups and strong property T for unital C^*-algebras. 相似文献
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11.
The Tracial Topological Rank of C*-Algebras 总被引:11,自引:0,他引:11
We introduce the notion of tracial topological rank for C*-algebras.In the commutative case, this notion coincides with the coveringdimension. Inductive limits of C*-algebrasof the form PMn(C(X))P,where X is a compact metric space with dim X k, and P is aprojection in Mn(C(X)), have tracial topological rank no morethan k. Non-nuclear C*-algebras can have small tracial topologicalrank. It is shown that if A is a simple unital C*-algebra withtracial topological rank k (< ), then
- (i) A is quasidiagonal,
- (ii) A has stable rank 1,
- (iii) A has weakly unperforatedK0(A),
- (iv) A has the following Fundamental Comparabilityof Blackadar:if p, q A are two projections with (p) < (q)for all tracialstates on A, then p q
- (ii) A has stable rank 1,
12.
给出了准Hilbert C~*_- 模中Dunkl-Williams不等式的进一步推广及其倒换,并刻画其等号成立的条件. 相似文献
13.
We show that every unitary representation of a discrete solvable virtually nilpotent group G is quasidiagonal. Roughly speaking, this says that every unitary representation of G approximately decomposes as a direct sum of finite dimensional approximate representations. In operator algebraic terms we show that C?(G) is strongly quasidiagonal. 相似文献
14.
We introduce a concept of the bounded rank (with respect to a positive constant) for unital C*-algebras as a modification of the usual real rank and present a series of conditions insuring that bounded and real ranks coincide. These observations are then used to prove that for a given n and K>0 there exists a separable unital C*-algebra ZnK such that every other separable unital C*-algebra of bounded rank with respect to K at most n is a quotient of ZnK. 相似文献
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16.
Edward Kissin 《Journal of Functional Analysis》2006,236(2):609-629
In this paper we consider automorphisms of the domains of closed *-derivations of C*-algebras and show that they extend to automorphisms of C*-algebras, so we call them diffeomorphisms. The diffeomorphisms generate transformations of the sets of closed *-derivations of C*-algebras. In this paper we study the subgroups of diffeomorphisms that define “bounded” shifts of derivations and the subgroups of the stabilizers of derivations. 相似文献
17.
Marius Dadarlat 《Advances in Mathematics》2009,222(5):1850-2880
Let X be a finite dimensional compact metrizable space. We study a technique which employs semiprojectivity as a tool to produce approximations of C(X)-algebras by C(X)-subalgebras with controlled complexity. The following applications are given. All unital separable continuous fields of C*-algebras over X with fibers isomorphic to a fixed Cuntz algebra On, n∈{2,3,…,∞}, are locally trivial. They are trivial if n=2 or n=∞. For n?3 finite, such a field is trivial if and only if (n−1)[A1]=0 in K0(A), where A is the C*-algebra of continuous sections of the field. We give a complete list of the Kirchberg algebras D satisfying the UCT and having finitely generated K-theory groups for which every unital separable continuous field over X with fibers isomorphic to D is automatically locally trivial or trivial. In a more general context, we show that a separable unital continuous field over X with fibers isomorphic to a KK-semiprojective Kirchberg C*-algebra is trivial if and only if it satisfies a K-theoretical Fell type condition. 相似文献
18.
C*-代数的*-同构一定是(完全)等距映射,反之不然.本文证明了C*-代数的实完全等距映射能够完全决定C*-代数*-同构的结论. 相似文献
19.
T. Ando 《Linear and Multilinear Algebra》1996,41(1):81-94
Motivated by an inequality of Choi for unital positive linear maps we introduce a quasi-order on the positive cone of a C*-algebra and present several intrinsic characterizations for it. We consider also another quasi-order based on an inequality of Kadison, and study interrelationship between those two quasi-orders. 相似文献
20.