Residually finite dimensional algebras and polynomial almost identities
نویسندگان
چکیده
منابع مشابه
Residually Finite Dimensional C*-algebras
A C*-algebra is called residually finite dimensional (RFD for brevity) if it has a separating family of finite dimensional representations. A C*-algebra A is said to be AF embeddable if there is an AF algebra B and a ∗-monomorphisms α : A→ B. In this note we discuss the question of AF embeddability of RFD algebras. Since a C*-subalgebra of a nuclear C*-algebra must be exact [Ki], the nonexact R...
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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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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 CA...
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ژورنال
عنوان ژورنال: Journal of Algebra and Its Applications
سال: 2020
ISSN: 0219-4988,1793-6829
DOI: 10.1142/s0219498822500384