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1.
We consider extension algebras of unital purely infinite simple C*-algebras by purely infinite simple stable C*-algebras. K-theory of such extension algebras is described. 相似文献
2.
Wilhelm Winter 《Inventiones Mathematicae》2010,179(2):229-301
We show that separable, simple, nonelementary, unital C*-algebras with finite decomposition rank absorb the Jiang–Su algebra
Z\mathcal{Z}
tensorially. This has a number of consequences for Elliott’s program to classify nuclear C*-algebras by their K-theory data. In particular, it completes the classification of C*-algebras associated to uniquely ergodic, smooth, minimal dynamical systems by their ordered K-groups. 相似文献
3.
A pro-C*-algebra is a (projective) limit of C*-algebras in the category of topological *-algebras. From the perspective of non-commutative geometry, pro-C*-algebras can be seen as non-commutative k-spaces. An element of a pro-C*-algebra is bounded if there is a uniform bound for the norm of its images under any continuous *-homomorphism into a C*-algebra. The *-subalgebra consisting of the bounded elements turns out to be a C*-algebra. In this paper, we investigate pro-C*-algebras from a categorical point of view. We study the functor (−)
b
that assigns to a pro-C*-algebra the C*-algebra of its bounded elements, which is the dual of the Stone-Čech-compactification. We show that (−)
b
is a coreflector, and it preserves exact sequences. A generalization of the Gelfand duality for commutative unital pro-C*-algebras is also presented. 相似文献
4.
We study the local operator space structure of nuclear C
*
-algebras. It is shown that a C
*
-algebra is nuclear if and only if it is an 𝒪ℒ∞,λ space for some (and actually for every) λ>6. The 𝒪ℒ∞ constant λ provides an interesting invariant
for nuclear C
*
-algebras. Indeed, if 𝒜 is a nuclear C
*
-algebra, then we have 1≤𝒪ℒ∞(𝒜)≤6, and if 𝒜 is a unital nuclear C
*
-algebra with , we show that 𝒜 must be stably finite. We also investigate the connection between the rigid 𝒪ℒ∞,1+ structure and the rigid complete order 𝒪ℒ∞,1+ structure on C
*
-algebras, where the latter structure has been studied by Blackadar and Kirchberg in their characterization of strong NF C
*
-algebras. Another main result of this paper is to show that these two local structrues are actually equivalent on unital
nuclear C
*
-algebras. We obtain this by showing that if a unital (nuclear) C
*
-algebra is a rigid 𝒪ℒ∞,1+ space, then it is inner quasi-diagonal, and thus is a strong NF algebra. It is also shown that if a unital (nuclear) C
*
-algebra is an 𝒪ℒ∞,1+ space, then it is quasi-diagonal, and thus is an NF algebra.
Received: 26 June 2001 / Revised version: 7 May 2002 / Published online: 10 February 2003
Mathematics Subject Classification (2000): 46L07, 46L05, 47L25
Junge and Ruan were partially supported by the National Science Foundation. Ozawa was supported by the Japanese Society for
Promotion of Science. 相似文献
5.
Let A , B be two unital C*-algebras. By using fixed pint methods, we prove that every almost unital almost linear mapping h : A → B which satisfies h(2 n uy) = h(2 n u)h(y) for all u ∈ U(A), all y ∈ A, and all n = 0, 1, 2, … , is a homomorphism. Also, we establish the generalized Hyers-Ulam-Rassias stability of *-homomorphisms on unital C*-algebras. 相似文献
6.
Qingzhai Fan 《Israel Journal of Mathematics》2013,195(2):545-563
We show that the Riesz interpolation property of the K 0-monoid of C*-algebras in the class Ω is inherited by simple unital C*-algebras in the class TAΩ, and the property of being an admissible target algebras of finite type in the class of Ω is inherited by unital C*-algebras in the class TAΩ. 相似文献
7.
The paper aims at developing a theory of nuclear (in the topological algebraic sense) pro-C*-algebras (which are inverse limits of C*-algebras) by investigating completely positive maps and tensor products. By using the structure of matrix algebras over a
pro-C*-algebra, it is shown that a unital continuous linear map between pro-C*-algebrasA andB is completely positive iff by restriction, it defines a completely positive map between the C*-algebrasb(A) andb(B) consisting of all bounded elements ofA andB. In the metrizable case,A andB are homeomorphically isomorphic iff they are matricially order isomorphic. The injective pro-C*-topology α and the projective pro-C*-topology v on A⊗B are shown to be minimal and maximal pro-C*-topologies; and α coincides with the topology of biequicontinous convergence iff eitherA orB is abelian. A nuclear pro-C*-algebraA is one that satisfies, for any pro-C*-algebra (or a C*-algebra)B, any of the equivalent requirements; (i) α =v onA ⊗B (ii)A is inverse limit of nuclear C*-algebras (iii) there is only one admissible pro-C*-topologyon A⊗B (iv) the bounded partb(A) ofA is a nuclear C⊗-algebra (v) any continuous complete state map A→B* can be approximated in simple weak* convergence by certain finite rank complete state maps. This is used to investigate permanence properties of nuclear pro-C*-algebras pertaining to subalgebras, quotients and projective and inductive limits. A nuclearity criterion for multiplier
algebras (in particular, the multiplier algebra of Pedersen ideal of a C*-algebra) is developed and the connection of this C*-algebraic nuclearity with Grothendieck’s linear topological nuclearity is examined. A σ-C*-algebraA is a nuclear space iff it is an inverse limit of finite dimensional C*-algebras; and if abelian, thenA is isomorphic to the algebra (pointwise operations) of all scalar sequences. 相似文献
8.
Choonkil PARK Jian Lian CUI 《数学学报(英文版)》2007,23(11):1919-1936
Let X and Y be vector spaces. The authors show that a mapping f : X →Y satisfies the functional equation 2d f(∑^2d j=1(-1)^j+1xj/2d)=∑^2dj=1(-1)^j+1f(xj) with f(0) = 0 if and only if the mapping f : X→ Y is Cauchy additive, and prove the stability of the functional equation (≠) in Banach modules over a unital C^*-algebra, and in Poisson Banach modules over a unital Poisson C*-algebra. Let A and B be unital C^*-algebras, Poisson C^*-algebras or Poisson JC^*- algebras. As an application, the authors show that every almost homomorphism h : A →B of A into is a homomorphism when h((2d-1)^nuy) =- h((2d-1)^nu)h(y) or h((2d-1)^nuoy) = h((2d-1)^nu)oh(y) for all unitaries u ∈A, all y ∈ A, n = 0, 1, 2,....
Moreover, the authors prove the stability of homomorphisms in C^*-algebras, Poisson C^*-algebras or Poisson JC^*-algebras. 相似文献
9.
M. V. Shchukin 《Russian Mathematics (Iz VUZ)》2011,55(7):81-88
In this paper we consider n-homogeneous C*-algebras generated by idempotents. We prove that a finitely generated unital n-homogeneous (when n is greater than or equals 2) C*-algebra A can be generated by a finite set of idempotents if and only if the algebra A contains at least one nontrivial idempotent. 相似文献
10.
The aim of the present (mostly expository) paper is to show the relationship of a generalization of Kazhdan’s property (T)
for C*-algebras introduced in our recent paper to that of B. Bekka. It is shown that our definition coincides with Bekka’s definition
for group C*-algebras of locally compact groups, whereas, in general, these definitions are distinct. Criteria for a C*-algebra to possess our property (T) are given. A number of examples of C*-algebras with and without property (T) are considered. Relations to K-theory are studied.
Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 13, No. 8, pp. 171–192, 2007. 相似文献
11.
A. M. Bikchentaev 《Mathematical Notes》2016,99(3-4):487-491
A new inequality for a trace on a unital C*-algebra is established. It is shown that the inequality obtained characterizes the traces in the class of all positive functionals on a unital C*-algebra. A new criterion for the commutativity of unital C*-algebras is proved. 相似文献
12.
We prove that every bounded local triple derivation on a unital C*-algebra is a triple derivation. A similar statement is established in the category of unital JB*-algebras. 相似文献
13.
Kazuyuki Sait 《Journal of Mathematical Analysis and Applications》2009,360(2):369-376
Akemann showed that any von Neumann algebra with a weak* separable dual space has a faithful normal representation on a separable Hilbert space. He posed the question: If a C*-algebra has a weak* separable state space, must it have a faithful representation on a separable Hilbert space? Wright solved this question negatively and showed that a unital C*-algebra has the weak* separable state space if and only if it has a unital completely positive map, into a type I factor on a separable Hilbert space, whose restriction to the self-adjoint part induces an order isomorphism. He called such a C*-algebra almost separably representable. We say that a unital C*-algebra is small if it has a unital complete isometry into a type I factor on a separable Hilbert space. In this paper we show that a unital C*-algebra is small if and only if the state spaces of all n by n matrix algebras over the C*-algebra are weak*-separable. It is natural to ask whether almost separably representable algebras are small or not. We settle this question positively for simple C*-algebras but the general question remains open. 相似文献
14.
ChunGilPARK 《数学学报(英文版)》2004,20(6):1047-1056
In this paper, we prove the generalized Hyers-Ulam-Rassias stability of universal Jensen‘s equations in Banach modules over a unital C^*-algebra. It is applied to show the stability of universal Jensen‘s equations in a Hilbert module over a unital C^*-algebra. Moreover, we prove the stability of linear operators in a Hilbert module over a unital C^*-algebra. 相似文献
15.
The N-Isometric Isomorphisms in Linear N-Normed C^*-Algebras 总被引:3,自引:3,他引:0
Chun-Gil PARK Themistocles M. RASSIAS 《数学学报(英文版)》2006,22(6):1863-1890
We prove the Hyers-Ulam stability of linear N-isometries in linear N-normed Banach mod- ules over a unital C^*-algebra. The main purpose of this paper is to investigate N-isometric C^*-algebra isomorphisms between linear N-normed C^*-algebras, N-isometric Poisson C^*-algebra isomorphisms between linear N-normed Poisson C^*-algebras, N-isometric Lie C^*-algebra isomorphisms between linear N-normed Lie C^*-algebras, N-isometric Poisson JC^*-algebra isomorphisms between linear N-normed Poisson JC^*-algebras, and N-isometric Lie JC^*-algebra isomorphisms between linear N-normed Lie JC^*-algebras.
Moreover, we prove the Hyers- Ulam stability of t:heir N-isometric homomorphisms. 相似文献
16.
On classifying monotone complete algebras of operators 总被引:1,自引:0,他引:1
We give a classification of “small” monotone complete C
*-algebras by order properties. We construct a corresponding semigroup. This classification filters out von Neumann algebras;
they are mapped to the zero of the classifying semigroup. We show that there are 2
c
distinct equivalence classes (where c is the cardinality of the continuum). This remains true when the classification is restricted to special classes of monotone
complete C
*-algebras e.g. factors, injective factors, injective operator systems and commutative algebras which are subalgebras of ℓ∞. Some examples and applications are given.
相似文献
17.
In a previous work, the authors showed that the C*-algebra C*(Λ) of a row-finite higher-rank graph Λ with no sources is simple if and only if Λ is both cofinal and aperiodic. In this
paper, we generalise this result to row-finite higher-rank graphs which are locally convex (but may contain sources). Our
main tool is Farthing’s “removing sources” construction which embeds a row-finite locally convex higher-rank graph in a row-finite
higher-rank graph with no sources in such a way that the associated C*-algebras are Morita equivalent. 相似文献
18.
Chun-Gil Park 《Bulletin of the Brazilian Mathematical Society》2005,36(3):333-362
Let X and Y be vector spaces. It is shown that a mapping f : X → Y satisfies the functional equation
if and only if the mapping f : X → Y is additive, and prove the Cauchy–Rassias stability of the functional equation (‡) in Banach modules over a unital C*-algebra. Let
and
be unital C*-algebras, Poisson C*-algebras, Poisson JC*-algebras or Lie JC*-algebras. As an application, we show that every almost homomorphism h :
→
of
into
is a homomorphism when h((d + 2)nuy) = h((d + 2)nu)h(y) or h((d + 2)nu ∘ y) = h((d + 2)nu) ∘ h(y) for all unitaries u ∈
, all y ∈
, and n = 0, 1, 2, • • • .
Moreover, we prove the Cauchy–Rassias stability of homomorphisms in C*-algebras, Poisson C*-algebras, Poisson JC*-algebras or Lie JC*-algebras.
Supported by Korea Research Foundation Grant KRF-2004-041-C00023. 相似文献
(‡) |
19.
20.
Kengo Matsumoto 《Mathematische Zeitschrift》2010,265(4):735-760
A C*-symbolic dynamical system ${(\mathcal{A}, \rho, \Sigma)}A C*-symbolic dynamical system (A, r, S){(\mathcal{A}, \rho, \Sigma)} consists of a unital C*-algebra A{\mathcal{A}} and a finite family { ra }a ? S{\{ \rho_\alpha \}_{\alpha \in \Sigma}} of endomorphisms ρ
α
of A{\mathcal{A}} indexed by symbols α of Σ satisfying some conditions. The endomorphisms ra, a ? S{\rho_\alpha, \alpha \in \Sigma } yield both a subshift Λ and a C*-algebra of a Hilbert C*-bimodule. The obtained C*-algebra is regarded as a crossed product of A{\mathcal{A}} by the subshift Λ. We will study simplicity condition of these C*-algebras. Some examples such as irrational rotation Cuntz–Krieger algebras will be studied. 相似文献