有限维实C^＊—代数

本文对有限维实Ｃ＾＊－代数的构造定理用算子代数方法给出了一个证明。     

A#H^＊rat为中心单代数的条件

本文用ＭｏｒｉｔａＣｏｎｔｅｘｔ的方法得到域上余ＦｒｏｂｅｎｉｕｓＨｏｐｆ代数Ｈ与Ｈ－余摸代数Ａ的Ｓｍａｓｈ积Ａ＃Ｈ＊ｒａｔ是中心单代数的条件：若Ａ／ＡＣｏＨ是Ｈ－Ｇａｌｏｉｓ扩张，且ＡＣｏＨ是中心单代数，则Ａ＃Ｈ＊ｒａｔ也是中心单代数，特别地，若ＡＣｏＨｋ，则Ａ＃Ｈ＊ｒａｔ是中心单代数，且为ｋ－空间Ａ上线性变换稠密环．作为推论给出Ｈ＃Ｈ＊ｒａｔ是本原中心单代数新的证明．     

有限维实C~＊－代数

本文对有限维实Ｃ￣＊－代数的构造定理用算子代数方法给出了一个证明。     

关于正定关联BCC—代数

首先指出在ＢＣＣ－代数中，下述两个条件并不等价：（１）（ｘ＊ｚ）＊（ｙ＊ｚ）＝（ｚ＊ｙ＿＊ｚ；（２）（ｘ＊ｙ＊ｙ＝ｘ＊ｙ。随后给出由Ｗ．Ａ．Ｄｕｄｅｋ１９９２年定义的正关联ＢＣＣ－代数的一个简单的公理系统。     

路代数的有向图特征与Brown—McMoy根

本文解决路代数中若干遗留问题，给出本原路代数，（右）Ｇｏｌｄｉｅ路代数的有向图特征，证明广义路代数的Ｒｒｏｗｎ－ＭｃＣｏｙ根与它的Ｊａｃｏｂｓｏｎ根不必重合。     

C^＊—模理论的若干结果

本文把代数结构与分析体系结合起来，运用同调的方法，较系统地确定了A上C^*－模的部分理论，这里A为复数域C上的交换C^*－代数。即不仅定义了与C^*－模有关的某些新概念，而且还得到了有关C^*－模的若干结果。     

关于余模代数的Hopf—Jacobson根的一些结果

设Ｈ是Ｈｏｐｆ代数，Ａ是右Ｈ－余模代数，若（，）满射，则Ｊ（Ａ＾ｃｏＨ）＝Ｌ＾Ｈ（Ａ）∩＾ｃｏＨ，而且，若Ｊ（Ａ）是余模理想，则Ｊ（Ａ＾ｃｏＨ）＝Ｊ＾Ｈ（Ａ）∩Ａ＾ｃｏＨ。     

代数自由积上的线性泛函的延拓

本文研究了C^＊-代数及其＊-稠子代数的＊-代数自由积．利用自由积的性质，得到了这两类自由积上的线性泛函到C^＊-代数（泛）自由积上的态延拓的充要条件，从而证明了这类延拓对于一般的C^＊-代数也是成立的．     

套代数中根理想的w*闭包

利用零化子的技巧,完全刻划了套代数中根Ｒ、ｒ的ω＊闭包,得到Ｒ＾Ｗ＊ｒ＝Ｈ＝（Ｒｒ∩Ｋ（Ｋ）＊＊,其中Ｒ＾Ｗ＊ｒ为Ｒｒ的Ｗ＊闭包,Ｋ＝｛Ｔ∈Ｒ（Ｋ）：Ｐ（Ｎ－）ＴＰ（Ｎ）＝０,Ａ↓Ｎ∈Ｎ｝;并且作为零化子和Ｒ＾Ｗ＊刻划的应用,给出了Ｒｒ中类Ｅｒｄｏｓ稠密性定理的一个新的证明和距离公式。     

关于BZ—代数中的群逆理想

证明了如下结果：如果Ａ是ＢＺ－代数Ｘ的一个理想，则Ｚ（Ａ）必是Ｘ的一个群逆理想，这里ＡＺ（Ａ）＝｛ｘ∈Ｘ｜０＊（０＊ｘ）∈Ａ｝．     

矩阵C*代数上的群作用与*-同构

通过矩阵C^*代数上的不变群作用,给出了决定C^*结构的一个充分条件。     

C~*-代数中的等价

在算子理论和算子代数的研究中,等价是一个很重要的工具,它对K-理论的研究和理解起着很重要的作用.寻找等价关系是研究不变量的一种方法,为了使大家更好的认识和学习C*-代数,我们在本文研究了算子代数中经常用到的代数等价、酉等价、同伦等几种等价之间的关系.     

C~*-index of observable algebras in G-spin model

In two-dimensional lattice spin systems in which the spins take values in afinite group G,one can define a field algebra F which carries an action of a Hopf algebraD(G),the double algebra of G and moreover,an action of D(G;H),which is a subalgebraof D(G)determined by a subgroup H of G,so that F becomes a modular algebra.Theconcrete construction of D(G;H)-invariant subspace A_H in F is given.By constructingthe quasi-basis of conditional expectation γ_G of A_H onto A_G,the C~*-index of γ_G is exactlythe index of H in G.     

Unitarily-invariant linear spaces in C*-algebras

Characterisations and containment results are given for linear subspaces of a unital C*-algebra that are invariant under conjugation by sets of unitary elements of the algebra. The (unitarily-invariant) linear span of the projections in a simple, unital C*-algebra having non-scalar projections is shown to contain all additive commutators of the algebra and, in certain cases, to be equal to the algebra.

     

线性Ce^＊—半范数的次可乘性

证明了具有单位元的*-代数上的任何线性Ce^*-半范数（或具有自伴核的线性Ce0^*-半范数）一定是C^*-半范数。     

交换的实W~*-代数

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］）．     

C*-index of observable algebras in <Emphasis Type="Italic">G</Emphasis>-spin model

In two-dimensional lattice spin systems in which the spins take values in a finite group G, one can define a field algebra F which carries an action of a Hopf algebra D(G), the double algebra of G and moreover, an action of D(G;H), which is a subalgebra of D(G) determined by a subgroup H of G, so that F becomes a modular algebra. The concrete construction of D(G;H)-invariant subspace A _H in F is given. By constructing the quasi-basis of conditional expectation γ _G of A _H onto A _G , the C*-index of γ _G is exactly the index of H in G.     

Topological *-algebras withC*-enveloping algebras II

UniversalC*-algebrasC*(A) exist for certain topological *-algebras called algebras with aC*-enveloping algebra. A Frechet *-algebraA has aC*-enveloping algebra if and only if every operator representation ofA mapsA into bounded operators. This is proved by showing that every unbounded operator representation π, continuous in the uniform topology, of a topological *-algebraA, which is an inverse limit of Banach *-algebras, is a direct sum of bounded operator representations, thereby factoring through the enveloping pro-C*-algebraE(A) ofA. Given aC*-dynamical system (G,A,α), any topological *-algebraB containingC _c (G,A) as a dense *-subalgebra and contained in the crossed productC*-algebraC*(G,A,α) satisfiesE(B) =C*(G,A,α). IfG = ℝ, ifB is an α-invariant dense Frechet *-subalgebra ofA such thatE(B) =A, and if the action α onB ism-tempered, smooth and by continuous *-automorphisms: then the smooth Schwartz crossed productS(ℝ,B,α) satisfiesE(S(ℝ,B,α)) =C*(ℝ,A,α). WhenG is a Lie group, theC ^∞-elementsC ^∞(A), the analytic elementsC ^ω(A) as well as the entire analytic elementsC ^є(A) carry natural topologies making them algebras with aC*-enveloping algebra. Given a non-unitalC*-algebraA, an inductive system of idealsI _α is constructed satisfyingA =C*-ind limI _α; and the locally convex inductive limit ind limI _α is anm-convex algebra with theC*-enveloping algebraA and containing the Pedersen idealK _a ofA. Given generatorsG with weakly Banach admissible relationsR, we construct universal topological *-algebraA(G, R) and show that it has aC*-enveloping algebra if and only if (G, R) isC*-admissible.     

Decomposition Rank of Subhomogeneous C*-Algebras

We analyze the decomposition rank (a notion of covering dimensionfor nuclear C*-algebras introduced by E. Kirchberg and the author)of subhomogeneous C*-algebras. In particular, we show that asubhomogeneous C*-algebra has decomposition rank n if and onlyif it is recursive subhomogeneous of topological dimension n,and that n is determined by the primitive ideal space. As an application, we use recent results of Q. Lin and N. C.Phillips to show the following. Let A be the crossed productC*-algebra coming from a compact smooth manifold and a minimaldiffeomorphism. Then the decomposition rank of A is dominatedby the covering dimension of the underlying manifold. 2000 MathematicsSubject Classification 46L85, 46L35.     

On the nuclearity of certain Cuntz‐Pimsner algebras

In the present paper, we give a short proof of the nuclearity property of a class of Cuntz‐Pimsner algebras associated with a Hilbert ??‐bimodule ??, where ?? is a separable and nuclear C *‐algebra. We assume that the left ??‐action on the bimodule ?? is given in terms of compact module operators and that ?? is direct summand of the standard Hilbert module over ?? (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)