THE INDUCED REPRESENTATION OF C^＊-GROUPOID DYNAMIC SYSTEMS

1.IntroductionandDefinitionsTheinducedrepresentationofgroupC*-algebrasfirstwasalgebraicallyintroducedbyfueffelin[3].P.Greenin[6]similiaxlyintroducedtheoneforcovariantdynamicsystem.TheinducedrepresentationofcrossedproductsbycoactionswasintroducedbyK.Mansfieldin[9].Using[8]wecanobtaintheinducedrepresentationofgrollpoidC*-algebrasin[1Ol.TherichapplicationofthesecanbefoundamongmanypapersrelativetotheC*-analysisofgroupoidandgroup.TheC*-groupoiddynamicsystemanditsreducedcrossedprod-uctwereintro…     

THE TRACE SPACE INVARIANT AND UNITARY GROUP OF C^＊—ALGEBRA

Let A be a unital C-algebra, n ∈ N ∪ {∞}. It is proved that the isomorphism △n : is isometric for some suitable distances. Asan application, the author has the split exact sequence with iA contractive (and isometric if n = ∞) under certain condition of A.     

THE UNIT BALL OF C^＊-ALGEBRA AND DIFFERENTIABILITY OF SUPPORT FUNCTION

In this paper we show that the unit ball of an infinite dimensional commutative C^*-algebra lacks strongly exposed points, so they have no predual. Also in the second part, we use the concept of strongly exposed points in the Frechet differentiability of support convex functions.     

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．     

ON THE CLASSIFICATION OF AF-ALGEBRAS AND THEIR DIMENSION GROUPS （Ⅱ）

ＯＮＴＨＥＣＬＡＳＳＩＦＩＣＡＴＩＯＮＯＦＡＦ－ＡＬＧＥＢＲＡＳＡＮＤＴＨＥＩＲＤＩＭＥＮＳＩＯＮＧＲＯＵＰＳ（Ⅱ）￥ＨＵＡＮＧＺＨＡＯＢＯＡｂｓｔｒａｃｔ：Ｔｈｉｓｐａｐｅｒｉｓａｃｏｎｔｉｎｕａｔｉｏｎｏｆ［１］．Ｉｔｇｉｖｅｓｓｏｍｅａｐｐｌｉ...     

Universal Jensen＇s Equations in Banach Modules over a C^＊-Algebra and Its Unitary Group

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.     

Complete Positivity of Elementary Operators on C^＊—algebras

1.IntroductionandPreliminariesInthispaper,AdenotesaC'-algebra.AnelementaryoperatoronAisamappingoftheformE:x-Zaixbi,whereaiandbiarefixedelementsofA.AnidempotenteinAiscalledi-lminimal,ifeAe=Ce.ThesocleofA,soc(A)isdefinedtobethetwo-sidedidealgeneratedbyallminimalidempotentsinAoroiftherearenone.AissaidtObeprimeifxAy=Oimpliesx=oory=oforallx,yinA.Aiscalledprimitiveifithasafaithfulirreduciblerepresenta-tion.LetAandBbeC'-algebras,alinearmap@:A-Biscalledpositiveifdi(a)ispositiveforallPositiv…     

ON THE APPROXIMATELY SIMILARITY OF OPERATORS

1.IntroductionInwhatfollows,allofHilbertspacesappearedinthispaperareinfinite-dimensionalseparablecomplexHilbertspace.IfHisaHilbertspace,thenC(n)denotestheC*--algebraofallboundedlinearoperatorsonHandK(H)denotesthesetofcompactoperatorsonn.TwooperatorsSandTarecalledapproximatelyequivalentifthereisasequenc{Un}ofunitaryoperatorssuchthatlIU:SUn--Tll-0(n-- co).SimilarlytwooperatosSandTareapproximatelysimilarifthereisasequence{Vn}ofinvertibleoperatorswithsup(llVn11,11VJ'11)相似文献   

Classification Theory for Inductive Limit C^＊-algebras

This paper is a survey on the recent work of the authors and their col-laborators on the Classification of Inductive Limit C*-algebras. Some examples are presented to explain several important ideas.     

THE K-THEORY AND THE CLASSIFICATION OF THE IRRATIONAL ROTATION GROUPOID C＊-ALGEBRAS

ＴＨＥＫＴＨＥＯＲＹＡＮＤＴＨＥＣＬＡＳＳＩＦＩＣＡＴＩＯＮＯＦＴＨＥＩＲＲＡＴＩＯＮＡＬＲＯＴＡＴＩＯＮＧＲＯＵＰＯＩＤＣＡＬＧＥＢＲＡＳＹＡＮＳＨＡＯＺＯＮＧＣＨＥＮＸＩＡＯＭＡＮＸＵＳＨＥＮＧＺＨＩＡｂｓｔｒａｃｔＴｈｅａｕｔｈｏｒ...     

Smale空间上的广群C~*-代数的迹

本文证明由拓扑混合的Smale空间上的渐进等价关系定义的广群C*-代数及其相应的Ruelle代数有唯一的迹态;在拓扑可迁的情形下,证明此C*-代数的迹态构成了一个单形,此单形顶点的个数等于“Smale谱分解”中基本空间的个数,单形的重心是该C*-代数的唯一的αa-不变迹态;此回答了I.Putnam的一个猜测.     

关于交换群上的Cayley有向图的正规性

Cayley有向图X=Cay(G,S)叫做正规的,如果G的右正则表示R(G)在X的全自同构群Aut(X)中正规,我们定出了交换群上的小度数的非正规的Cayley有向图, 并给出了一个猜想．应用这个结果,给出了pn(n≤2)个点上的度数不超过3的有向对称图的分类,这里p是一个奇素数．     

短区间上非同构有限Abel群的个数

用算术函数ａ（ｎ）表示ｎ阶非同构Ａｂｅｌ群的个数，令Ａｋ（ｘ）＝∑／ｎ≤ｘ／ａ（ｎ）＝ｋ １，Ａｋ（ｘ；ｈ）＝Ａｋ（ｘ＋ｊ）－Ａｋ（ｘ）。     

有限群的中心化子指数

假定有限群A互索地作用在G上,设H≤G且x=ηG,其中x∈Irr(G),η∈Irr(H)都是A-不变的,设fA(G)=|G:CG(A)|.I.M.Isaacs和G.Navarro曾猜想fA(G)≤fA(H)s,其中s是某一常数.本文证明了:若G是奇阶的且可诱导的,那么存在一个标准三元组(G,R,A)满足fA(G)≤fA(R)β, 其中3.24<β<3.25.若(G,H,A)是一个标准三元组,且不等式fA(G)≤fA(H)β对任意索阶群A 都成立,其中β是一个常数,那么这一不等式对所有可解群A都成立.     

计算对称群S6的所有子群

利用电子计算机,通过计算的方法,获得了对称群S6共有1455个子群,且每个子群给出了一组生成元素,同时给出了计算的流程图及方法步骤。     

THE FUNDAMENTAL GROUP OFTHE AUTOMORPHISM GROUP OFA NONCOMMUTATIVE TORUSTHE FUNDAMENTAL GROUP OFTHE AUTOMORPHISM GROUP OFA NONCOMMUTATIVE TORU

1. IntroductionGiven a locally compact abelian group G and a multiplier p on G, one can associate tothem the twisted group C*-algebra C*(G, p), which is the universal object for unitary prepresentations of G. C* (Zm, p) is said to be a noncommutative torns of rank m and denotedby A.. The multiplier p determines a subgroup S. of G, called its symmetry group, andthe multiplier p is called totally skew if the symmetry group S. is trivial. And A. is calledcompletely irrational if p is totally…     

ASYMPTOTIC PROPERTIES OF ELEMENTS IN GROUP RINGS OF FINITE GROUPS

A relation between algebraic degrees of eigenvalues of an element in the group ring Z G of a finite group G and their multiplicities is obtained. This result can be regarded as a theorem on asymptotic behavior of parameters in group rings of finite groups which is a parallel result of several well known theorems concerning the relationships of parameters in finite groups.