Extensions of C *-Algebras and Quasidiagonality
نویسندگان
چکیده
منابع مشابه
Extensions of C∗-algebras and Quasidiagonality
Using extension theory and recent results of Elliott and Gong we exhibit new classes of nuclear stably finite C∗-algebras , which have real rank zero and stable rank one, and are classified by K-theoretical data. Various concepts of quasidiagonality are employed to show that these C*-algebras are not inductive limits of (sub)homogeneous C∗-algebras.
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15 صفحه اولExtensions 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 کاملExtensions, Restrictions, and Representations of States on C*-algebras
In the first three sections the question of when a pure state g on a C*-subalgebra B of a C*-algebra A has a unique state extension is studied. It is shown that an extension/is unique if and only if inf||6(o — f(a)\)b\\ = 0 for each a in A, where the inf is taken over those b in B such that 0 < b < 1 and g(b) =* 1. The special cases where B is maximal abelian and/or A — B(H) are treated in more...
متن کامل(apd)–property of C∗–algebras by Extensions of C∗–algebras with (apd)
A unital C∗–algebra A is said to have the (APD)–property if every nonzero element in A has the approximate polar decomposition. Let J be a closed ideal of A. Suppose that J̃ and A/J have (APD). In this paper, we give a necessary and sufficient condition that makes A have (APD). Furthermore, we show that if RR(J ) = 0 and tsr(A/J ) = 1 or A/J is a simple purely infinite C∗–algebra, then A has (APD).
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ژورنال
عنوان ژورنال: Journal of the London Mathematical Society
سال: 1996
ISSN: 0024-6107
DOI: 10.1112/jlms/53.3.582