We study diagonal invariant ideals of topologically graded C*-algebras over discrete groups. Since all Toeplitz algebras defined on discrete groups are topologically graded, the results in this paper have improved the...We study diagonal invariant ideals of topologically graded C*-algebras over discrete groups. Since all Toeplitz algebras defined on discrete groups are topologically graded, the results in this paper have improved the first author's previous works on this topic.展开更多
First, that prime C~* -algebras with countable primitive ideals are all primitive C*-algebras is proved. Then the proof that prime C~* -algebras with property RR(A) = 0 are all primitive C~*-algebras is given.
Let A be a unital simple C-algebra of real rank zero,stable rank one,with weakly unperforated K<sub>0</sub>(A)and unique normalized quasi-trace τ,and let X be a compact metric space.We show that two mon...Let A be a unital simple C-algebra of real rank zero,stable rank one,with weakly unperforated K<sub>0</sub>(A)and unique normalized quasi-trace τ,and let X be a compact metric space.We show that two monomorphisms Φ,Ψ:C(X)→A are approximately unitarily equivalent if and only if Φ and Ψ induce the same element in KL(C(X),A)and the two linear functionals τ ο Φ and τ ο Φ are equal.We also show that,with an injectivity condition,an almost multiplicative morphism from C(X) into A with vanishing KK-obstacle is close to a homomorphism.展开更多
It is shown that every almost *-homomorphism h : A→B of a unital JC*-algebra A to a unital JC*-algebra B is a *-homomorphism when h(rx) = rh(x) (r 〉 1) for all x∈A, and that every almost linear mapping h...It is shown that every almost *-homomorphism h : A→B of a unital JC*-algebra A to a unital JC*-algebra B is a *-homomorphism when h(rx) = rh(x) (r 〉 1) for all x∈A, and that every almost linear mapping h : A→B is a *-homomorphism when h(2^nu o y) - h(2^nu) o h(y), h(3^nu o y) - h(3^nu) o h(y) or h(q^nu o y) = h(q^nu) o h(y) for all unitaries u ∈A, all y ∈A, and n = 0, 1,.... Here the numbers 2, 3, q depend on the functional equations given in the almost linear mappings. We prove that every almost *-homomorphism h : A→B of a unital Lie C*-algebra A to a unital Lie C*-algebra B is a *-homomorphism when h(rx) = rh(x) (r 〉 1) for all x ∈A.展开更多
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...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.展开更多
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...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.展开更多
Extending the notion of property T of finite von Neumann algebras to general yon Neu- mann algebras, we define and study in this paper property T** for (possibly non-unital) C*-algebras. We obtain several results...Extending the notion of property T of finite von Neumann algebras to general yon Neu- mann algebras, we define and study in this paper property T** for (possibly non-unital) C*-algebras. We obtain several results of property T** parallel to those of property T for unital C*-algebras. Moreover, we show that a discrete group F has property T if and only if the group C*-algebra C*(F) (or equivalently, the reduced group C*-algebra C*(F)) has property T**. We also show that the compact operators K(g2) has property T** but co does not have property T**.展开更多
The paper is devoted to the study of generalized inductive limit of C*-algebras with coherent maps being completely positive contractions of order zero: the nuclear dimension of generalized inductive limit of C*-al...The paper is devoted to the study of generalized inductive limit of C*-algebras with coherent maps being completely positive contractions of order zero: the nuclear dimension of generalized inductive limit of C*-algebras with finite nuclear dimension is finite; the generalized inductive limits of C*-algebras with the α-comparison property also have the s-comparison property.展开更多
In this paper,we show that a topologically irreducible * representation of a real C~*- algebra is also algebraically irreducible.Moreover,the properties of pure real states on a real C~*- algebra and their left kernel...In this paper,we show that a topologically irreducible * representation of a real C~*- algebra is also algebraically irreducible.Moreover,the properties of pure real states on a real C~*- algebra and their left kernels are discussed.展开更多
The authors consider the irreducibility of the Cowen-Douglas operator T. It is proved that T is irreducible iff the unital C*-algebra generated by some non-zero blocks in the decomposition of T with respect to (Ker Tn...The authors consider the irreducibility of the Cowen-Douglas operator T. It is proved that T is irreducible iff the unital C*-algebra generated by some non-zero blocks in the decomposition of T with respect to (Ker Tn+1 Ker Tn) is M.(C).展开更多
Let (A, Z, α) be a C<sup>*</sup>-dynamical system, and α<sup>n</sup>=id (n is a fixed positive integer). A natural problem is how the C<sup>*</sup>-crossed product A ×<...Let (A, Z, α) be a C<sup>*</sup>-dynamical system, and α<sup>n</sup>=id (n is a fixed positive integer). A natural problem is how the C<sup>*</sup>-crossed product A ×<sub>α</sub>Z relates to A×<sub>α</sub>Z<sub>n</sub>. The answer is the following: A×<sub>α</sub>Z≌M<sub>A×<sub>α</sub>Z<sub>n</sub></sub>,where M<sub>A×<sub>α</sub>Z<sub>n</sub></sub> is the mapping torus of , and (A×<sub>α</sub>Z<sub>n</sub>, <sub>n</sub>, )is the dual system展开更多
基金Supported by the National Natural Science Foundation of China(10371051)
文摘We study diagonal invariant ideals of topologically graded C*-algebras over discrete groups. Since all Toeplitz algebras defined on discrete groups are topologically graded, the results in this paper have improved the first author's previous works on this topic.
文摘First, that prime C~* -algebras with countable primitive ideals are all primitive C*-algebras is proved. Then the proof that prime C~* -algebras with property RR(A) = 0 are all primitive C~*-algebras is given.
基金Research partially supported by NSF Grants DMS 93-01082(H.L)and DMS-9401515(G.G)This work was reported by the first named author at West Coast Operator Algebras Seminar(Sept.1995,Eugene,Oregon)
文摘Let A be a unital simple C-algebra of real rank zero,stable rank one,with weakly unperforated K<sub>0</sub>(A)and unique normalized quasi-trace τ,and let X be a compact metric space.We show that two monomorphisms Φ,Ψ:C(X)→A are approximately unitarily equivalent if and only if Φ and Ψ induce the same element in KL(C(X),A)and the two linear functionals τ ο Φ and τ ο Φ are equal.We also show that,with an injectivity condition,an almost multiplicative morphism from C(X) into A with vanishing KK-obstacle is close to a homomorphism.
基金Grant No.R05-2003-000-10006-0 from the Basic Research Program of the Korea Science & Engineering Foundation.NNSF of China and NSF of Shanxi Province
文摘It is shown that every almost *-homomorphism h : A→B of a unital JC*-algebra A to a unital JC*-algebra B is a *-homomorphism when h(rx) = rh(x) (r 〉 1) for all x∈A, and that every almost linear mapping h : A→B is a *-homomorphism when h(2^nu o y) - h(2^nu) o h(y), h(3^nu o y) - h(3^nu) o h(y) or h(q^nu o y) = h(q^nu) o h(y) for all unitaries u ∈A, all y ∈A, and n = 0, 1,.... Here the numbers 2, 3, q depend on the functional equations given in the almost linear mappings. We prove that every almost *-homomorphism h : A→B of a unital Lie C*-algebra A to a unital Lie C*-algebra B is a *-homomorphism when h(rx) = rh(x) (r 〉 1) for all x ∈A.
基金Grant No. F01-2006-000-10111-0 from the Korea Science & Engineering FoundationThe second author is supported by National Natural Science Foundation of China (No.10501029)+1 种基金Tsinghua Basic Research Foundation (JCpy2005056)the Specialized Research Fund for Doctoral Program of Higher Education
文摘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.
基金the National Natural Science Foundation of China(No.10301004)Excellent Young Scholars Research Fund of Beijing Institute of Technology(00Y07-25)
文摘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.
文摘Extending the notion of property T of finite von Neumann algebras to general yon Neu- mann algebras, we define and study in this paper property T** for (possibly non-unital) C*-algebras. We obtain several results of property T** parallel to those of property T for unital C*-algebras. Moreover, we show that a discrete group F has property T if and only if the group C*-algebra C*(F) (or equivalently, the reduced group C*-algebra C*(F)) has property T**. We also show that the compact operators K(g2) has property T** but co does not have property T**.
基金Supported by NSFC(Grant No.11371279)by the Fundamental Research Funds for the Central Universities
文摘The paper is devoted to the study of generalized inductive limit of C*-algebras with coherent maps being completely positive contractions of order zero: the nuclear dimension of generalized inductive limit of C*-algebras with finite nuclear dimension is finite; the generalized inductive limits of C*-algebras with the α-comparison property also have the s-comparison property.
基金Partially supported by the National Natural Science Foundation of China.
文摘In this paper,we show that a topologically irreducible * representation of a real C~*- algebra is also algebraically irreducible.Moreover,the properties of pure real states on a real C~*- algebra and their left kernels are discussed.
文摘The authors consider the irreducibility of the Cowen-Douglas operator T. It is proved that T is irreducible iff the unital C*-algebra generated by some non-zero blocks in the decomposition of T with respect to (Ker Tn+1 Ker Tn) is M.(C).
基金Project partially supported by the National Natural Science Foundation of China.
文摘Let (A, Z, α) be a C<sup>*</sup>-dynamical system, and α<sup>n</sup>=id (n is a fixed positive integer). A natural problem is how the C<sup>*</sup>-crossed product A ×<sub>α</sub>Z relates to A×<sub>α</sub>Z<sub>n</sub>. The answer is the following: A×<sub>α</sub>Z≌M<sub>A×<sub>α</sub>Z<sub>n</sub></sub>,where M<sub>A×<sub>α</sub>Z<sub>n</sub></sub> is the mapping torus of , and (A×<sub>α</sub>Z<sub>n</sub>, <sub>n</sub>, )is the dual system