Tracial Limit of C^＊-algebras

A new limit of C^*-algebras, the tracial limit, is introduced in this paper. We show that a separable simple C^*-algebra A is a tracial limit of C^*-algebras in Z-(k) if and only if A has tracial topological rank no more than k. We present several known results using the notion of tracial limits.     

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.     

Pairing and Quantum Double of Finite Hopf C^＊-Algebras

This paper defines a pairing of two finite Hopf C^＊-algebras A and B, and investigates the interactions between them. If the pairing is non-degenerate, then the quantum double construction is given. This construction yields a new finite Hopf C^＊-algebra D（A, B）. The canonical embedding maps of A and B into the double are both isometric.     

Approximately Linear Mappings in Banach Modules over a C^＊-algebra

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.     

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.     

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 INVARIANT CONTINUOUS-TRACE C^＊-ALGEBRAS BY THE ACTIONS OF COMPACT ABELIAN GROUPS

1.IntroductionLet(A,G,a)beaC*-dynamicsystem.TherelationbetweenAxosGandAhasbeenstudiedforalongtime,andconsiderableprogresshasbeenmade.SpeciallyifAisacontinuous-traceC*-algebra,I.Raeburnandhiscollaboratorsgotrichresultsseveralyearsago.Forexample,[17]and119]saythatifAisparacompact,Gisabelianandaislocallyunitary,thenAiscontinuous-traceiffAxosGiscontinuous-trace.Inotherdirection,therelationbetweenAxosGandA\"withGcompacthasalsobeenstudiedformanyyears.Themovementofthispaperistoinvestigatethec…     

HYERS—ULAM—RASSIAS STABILITY OF QUADRATIC FUNCTIONAL EQUATIONS IN BANACH MODULES OVER A C^＊—ALGEBRA

The authors prove the Hyers-Ulam-Rassias stability of the quadratic mapping in Banach modules over a unital C*-algebra, and prove the Hyers-Ulam-Rassias stability of the quadratic mapping in Banach modules over a unital Banach algebra.     

Approximate （m,n）-Cauchy-Jensen Additive Mappings in C^＊-algebras

Concerning the stability problem of functional equations, we introduce a general (m, n)-Cauchy-Jensen functional equation and establish new theorems about the Hyers-Ulam stability of general (m, n)-Cauchy-Jensen additive mappings in C*-algebras, which generalize the results obtained for Cauchy-Jensen type additive mappings.     

Factorization of EP elements in C*-algebras

We offer some extensions to C*-algebra elements of factorization properties of EP operators on a Hilbert space.     

单的迹稳定秩一C*-代数的消去性质

本文证明了一个单的有单位元的迹稳定秩一的C*-代数具有消去律,利用此结果证明了单的有单位元的迹稳定秩一的C*-代数是稳定秩一的.最后讨论了迹稳定秩一的C*-代数的K0群的性质.     

Positive and real-positive solutions to the equation axa*=c in C*-algebras

We obtain new representations for the general positive and real-positive solutions of the equation axa*=c in a C*-algebra using the characterization of positivity based on a matrix representation of an element and the generalized Schur complement. Applications to the equation AXA*=C for operators between Hilbert spaces and for finite matrices are given.     

Problem of invariant subspaces in C*-algebras

Let A be a separable simple C*-algebra. For each a(≠0) in A, there exists a separable faithful and irreducible * representation (π, Hπ) on A such that π(a) has a non-trivial invariant subspace in Hπ.     

Bessel-type inequalities in Hilbert C *-modules

Regarding the generalizations of the Bessel inequality in Hilbert spaces which are due to Bombieri and Boas–Bellman, we obtain a version of the Bessel inequality and some generalizations of this inequality in the framework of Hilbert C *-modules.