Quasidiagonal operator algebras
نویسندگان
چکیده
منابع مشابه
On Quasidiagonal C-algebras
We give a detailed survey of the theory of quasidiagonal C∗-algebras. The main structural results are presented and various functorial questions around quasidiagonality are discussed. In particular we look at what is currently known (and not known) about tensor products, quotients, extensions, free products, etc. of quasidiagonal C∗-algebras. We also point out how quasidiagonality is connected ...
متن کاملOn the Approximation of Quasidiagonal C*-Algebras
Let A be a separable exact quasidiagonal C*-algebra. Suppose that ?: A L(H) is a faithful representation whose image does not contain nonzero compact operators. Then there exists a sequence .n : A L(H) of completely positive contractions such that &?(a)&.n(a)& 0 for all a # A, and the C*-algebra generated by .n(A) is finite dimensional for each n. As an application it is shown that if the C*-al...
متن کاملIrreducible Representations of Inner Quasidiagonal C*-algebras
It is shown that a separable C*-algebra is inner quasidiagonal if and only if it has a separating family of quasidiagonal irreducible representations. As a consequence, a separable C*-algebra is a strong NF algebra if and only if it is nuclear and has a separating family of quasidiagonal irreducible representations. We also obtain some permanence properties of the class of inner quasidiagonal C...
متن کاملExtensions of Quasidiagonal C * -algebras and K-theory
Let 0 → I → E → B → 0 be a short exact sequence of C*-algebras whereE is separable, I is quasidiagonal (QD) andB is nuclear, QD and satisfies the UCT. It is shown that if the boundary map ∂ : K1(B) → K0(I) vanishes then E must be QD also. A Hahn-Banach type property for K0 of QD C ∗-algebras is also formulated. It is shown that every nuclear QD C∗-algebra has this K0Hahn-Banach property if and ...
متن کاملOperator Algebras
Notice that the left-hand side of the third equation is the sum of the left-hand sides of the first two. As a result, no solution to the system exists unless a + b = c. But if a + b = c, then any solution of the first two equations is also a solution of the third; and in any linear system involving more unknowns than equations, solutions, when they exist, are never unique. In the present case, ...
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ژورنال
عنوان ژورنال: Illinois Journal of Mathematics
سال: 1991
ISSN: 0019-2082
DOI: 10.1215/ijm/1255987790