Residually Finite Dimensional C*-algebras and Subquotients of the Car Algebra
نویسندگان
چکیده
It is proved that the cone of a separable nuclearly embeddable residually finite-dimensional C*-algebra embeds in the CAR algebra (the UHF algebra of type 2∞). As a corollary we obtain a short new proof of Kirchberg’s theorem asserting that a separable unital C*-algebra A is nuclearly embeddable if and only there is a semisplit extension 0 → J → E → A → 0 with E a unital C*-subalgebra of the CAR algebra and the ideal J an AF-algebra. The new proof does not rely on the lifting theorem of Effros and Haagerup.
منابع مشابه
Operator Spaces and Residually Finite-dimensional C * -algebras
For every operator space X the C∗-algebra containing it in a universal way is residually finite-dimensional (that is, has a separating family of finitedimensional representations). In particular, the free C∗-algebra on any normed space so is. This is an extension of an earlier result by Goodearl and Menal, and our short proof is based on a criterion due to Exel and Loring.
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