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 i...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 , two positive elements (projections, partial isometries, unitary elements, respectively) aˉ, ˉb in A/I, and a positive element (projection, partial isometry, unitary element, respectively) a which is a lifting of aˉ, there is a positive element (projection, partial isometry, unitary element, respectively) b in A which is a lifting of ˉb such that ab < aˉˉb + . As an application, it is shown that for any positive numbers and uˉ in U(A/I)0, there exists u in U(A)0 which is a lifting of uˉ such that cel(u) < cel(uˉ) + .展开更多
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 , two positive elements (projections, partial isometries, unitary elements, respectively) aˉ, ˉb in A/I, and a positive element (projection, partial isometry, unitary element, respectively) a which is a lifting of aˉ, there is a positive element (projection, partial isometry, unitary element, respectively) b in A which is a lifting of ˉb such that ab < aˉˉb + . As an application, it is shown that for any positive numbers and uˉ in U(A/I)0, there exists u in U(A)0 which is a lifting of uˉ such that cel(u) < cel(uˉ) + .
