This paper introduced the concept of generalized quasidiagonal extension of C^(*)-algebras and gave some basic properties.We show that the extension algebra preserves quasidiagonality and finitary in generalized quasi...This paper introduced the concept of generalized quasidiagonal extension of C^(*)-algebras and gave some basic properties.We show that the extension algebra preserves quasidiagonality and finitary in generalized quasidiagonal extension.We give also an example of generalized quasidiagonal extension,which is not quasidiagonal extension.展开更多
This paper introduce the concept of locally quasidiagonal extension of C^(*)-algebras and give some basic properties.We use the method of analogy,based on some properties possessed by quasidiagonal extensions,we inves...This paper introduce the concept of locally quasidiagonal extension of C^(*)-algebras and give some basic properties.We use the method of analogy,based on some properties possessed by quasidiagonal extensions,we investigate whether local quasidiagonal extensions still retain these properties.We then show that an extension of a locally AF algebra by a locally AF algebra is a locally quasidiagonal extension.展开更多
Perturbation problem of operator algebras was first introduced by Kadison and Kastler. In this short note, we consider the uniform perturbation of two classes of operator algebras, i.e., MF algebras and quasidiagonal ...Perturbation problem of operator algebras was first introduced by Kadison and Kastler. In this short note, we consider the uniform perturbation of two classes of operator algebras, i.e., MF algebras and quasidiagonal C*-algebras. We show that the sets of MF algebras and quasidiagonal C*-algebras of a given C*-algebra are closed under the perturbation of uniform norm.展开更多
Let A and B be C^＊-algebras. An extension of B by A is a short exact sequence O→A→E→B→O. （＊） Suppose that A is an AT-algebra with real rank zero and B is any AT-algebra. We prove that E is an AT-algebra if an...Let A and B be C^＊-algebras. An extension of B by A is a short exact sequence O→A→E→B→O. （＊） Suppose that A is an AT-algebra with real rank zero and B is any AT-algebra. We prove that E is an AT-algebra if and only if the extension （＊） is quasidiagonal.展开更多
Suppose that 0→ I→ A→ A/I→ 0 is a tracially quasidiagonal extension of C*-algebras. In this paper, the authors give two descriptions of the K_0, K_1 index maps which are induced by the above extension and show tha...Suppose that 0→ I→ A→ A/I→ 0 is a tracially quasidiagonal extension of C*-algebras. In this paper, the authors give two descriptions of the K_0, K_1 index maps which are induced by the above extension and show that for any ∈ > 0, any τ in the tracial state space of A/I and any projection p ∈ A/I(any unitary u ∈ A/I), there exists a projection p ∈ A(a unitary u ∈ A) such that |τ(p)-τ(π(p))| < ∈(|τ(u)-τ(π(u))| < ∈).展开更多
In the current article,we prove the crossed product C^*-algebra by a Rokhlin action of finite group on a strongly quasidiagonal C^*-algebra is strongly quasidiagonal again.We also show that a just-infinite C^*-algebra...In the current article,we prove the crossed product C^*-algebra by a Rokhlin action of finite group on a strongly quasidiagonal C^*-algebra is strongly quasidiagonal again.We also show that a just-infinite C^*-algebra is quasidiagonal if and only if it is inner quasidiagonal.Finally,we compute the topological free entropy dimension in just-infinite C^*-algebras.展开更多
Let 0 → I → A → A/I → 0 be a short exact sequence of C*-algebras with A unital. Suppose that the extension 0 → I → A → A/I → 0 is quasidiagonal, then it is shown that any positive element (projection, partial ...Let 0 → I → A → A/I → 0 be a short exact sequence of C*-algebras with A unital. Suppose that the extension 0 → I → A → A/I → 0 is quasidiagonal, then it is shown that any positive element (projection, partial isometry, unitary element, respectively) in A/I has a lifting with the same form which commutes with some quasicentral approximate unit of I consisting of projections. Furthermore, it is shown that for any given positive number ε, two positive elements (projections, partial isometries, unitary elements, respectively) $ \bar a,\bar b $ in A/I, and a positive element (projection, partial isometry, unitary element, respectively) a which is a lifting of $ \bar a $ , there is a positive element (projection, partial isometry, unitary element, respectively) b in A which is a lifting of $ \bar b $ such that ∥a?b∥ < $ \left\| {\bar a - \bar b} \right\| + \varepsilon $ . As an application, it is shown that for any positive numbers ε and $ \bar u $ in U(A/I) 0 , there exists u in U(A)0 which is a lifting of $ \bar u $ such that cel(u) < cel $ (\bar u) + \varepsilon $ .展开更多
Let X be a noncompact discrete metric space with bounded geometry. Associated with X are two C*-algebras, the so-called uniform Roe algebra B*(X) and coarse Roe algebra C*(X), which arose from the index theory on nonc...Let X be a noncompact discrete metric space with bounded geometry. Associated with X are two C*-algebras, the so-called uniform Roe algebra B*(X) and coarse Roe algebra C*(X), which arose from the index theory on noncompact complete Riemannian manifolds. In this paper, we describe the quasidiagonality of B*(X) and C*(X) in terms of coarse geometric invariants. Some necessary and suficient conditions are given, which involve the Fredholm index and coarse connectedness of metric spaces.展开更多
Let 0 →I → A →A/I →0 be a short exact sequence of C^＊-algebras with A unital. Suppose that I has tracial topological rank no more than one and A/I belongs to a class of certain C^＊-algebras. We show that A has t...Let 0 →I → A →A/I →0 be a short exact sequence of C^＊-algebras with A unital. Suppose that I has tracial topological rank no more than one and A/I belongs to a class of certain C^＊-algebras. We show that A has trazial topological rank no more than one if the extension is quasidiagonal, and A has the property （P1） if the extension is tracially quasidiagonal.展开更多
基金Supported by NSF of Jiangsu Province(No.BK20171421)。
文摘This paper introduced the concept of generalized quasidiagonal extension of C^(*)-algebras and gave some basic properties.We show that the extension algebra preserves quasidiagonality and finitary in generalized quasidiagonal extension.We give also an example of generalized quasidiagonal extension,which is not quasidiagonal extension.
文摘This paper introduce the concept of locally quasidiagonal extension of C^(*)-algebras and give some basic properties.We use the method of analogy,based on some properties possessed by quasidiagonal extensions,we investigate whether local quasidiagonal extensions still retain these properties.We then show that an extension of a locally AF algebra by a locally AF algebra is a locally quasidiagonal extension.
文摘Perturbation problem of operator algebras was first introduced by Kadison and Kastler. In this short note, we consider the uniform perturbation of two classes of operator algebras, i.e., MF algebras and quasidiagonal C*-algebras. We show that the sets of MF algebras and quasidiagonal C*-algebras of a given C*-algebra are closed under the perturbation of uniform norm.
文摘Let A and B be C^＊-algebras. An extension of B by A is a short exact sequence O→A→E→B→O. （＊） Suppose that A is an AT-algebra with real rank zero and B is any AT-algebra. We prove that E is an AT-algebra if and only if the extension （＊） is quasidiagonal.
基金supported by the National Natural Science Foundation of China(Nos.11871375,11371279,11601339)Zhejiang Provincial Natural Science Foundation of China(No.LY13A010021)
文摘Suppose that 0→ I→ A→ A/I→ 0 is a tracially quasidiagonal extension of C*-algebras. In this paper, the authors give two descriptions of the K_0, K_1 index maps which are induced by the above extension and show that for any ∈ > 0, any τ in the tracial state space of A/I and any projection p ∈ A/I(any unitary u ∈ A/I), there exists a projection p ∈ A(a unitary u ∈ A) such that |τ(p)-τ(π(p))| < ∈(|τ(u)-τ(π(u))| < ∈).
文摘In the current article,we prove the crossed product C^*-algebra by a Rokhlin action of finite group on a strongly quasidiagonal C^*-algebra is strongly quasidiagonal again.We also show that a just-infinite C^*-algebra is quasidiagonal if and only if it is inner quasidiagonal.Finally,we compute the topological free entropy dimension in just-infinite C^*-algebras.
基金supported by National Natural Science Foundation of China (Grant No. 10771161)
文摘Let 0 → I → A → A/I → 0 be a short exact sequence of C*-algebras with A unital. Suppose that the extension 0 → I → A → A/I → 0 is quasidiagonal, then it is shown that any positive element (projection, partial isometry, unitary element, respectively) in A/I has a lifting with the same form which commutes with some quasicentral approximate unit of I consisting of projections. Furthermore, it is shown that for any given positive number ε, two positive elements (projections, partial isometries, unitary elements, respectively) $ \bar a,\bar b $ in A/I, and a positive element (projection, partial isometry, unitary element, respectively) a which is a lifting of $ \bar a $ , there is a positive element (projection, partial isometry, unitary element, respectively) b in A which is a lifting of $ \bar b $ such that ∥a?b∥ < $ \left\| {\bar a - \bar b} \right\| + \varepsilon $ . As an application, it is shown that for any positive numbers ε and $ \bar u $ in U(A/I) 0 , there exists u in U(A)0 which is a lifting of $ \bar u $ such that cel(u) < cel $ (\bar u) + \varepsilon $ .
基金supported by National Natural Science Foundation of China (Grant No. 10871140)
文摘Let X be a noncompact discrete metric space with bounded geometry. Associated with X are two C*-algebras, the so-called uniform Roe algebra B*(X) and coarse Roe algebra C*(X), which arose from the index theory on noncompact complete Riemannian manifolds. In this paper, we describe the quasidiagonality of B*(X) and C*(X) in terms of coarse geometric invariants. Some necessary and suficient conditions are given, which involve the Fredholm index and coarse connectedness of metric spaces.
基金supported by National Natural Science Foundation of China (Grant No. 11071188)
文摘Let 0 →I → A →A/I →0 be a short exact sequence of C^＊-algebras with A unital. Suppose that I has tracial topological rank no more than one and A/I belongs to a class of certain C^＊-algebras. We show that A has trazial topological rank no more than one if the extension is quasidiagonal, and A has the property （P1） if the extension is tracially quasidiagonal.
