On the Approximation of Quasidiagonal C*-Algebras
نویسنده
چکیده
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*-algebra generated by a quasidiagonal operator T is exact and does not contain any nontrivial compact operator, then T is norm-limit of block-diagonal operators D=D1 D2 } } } with supi rank(D i)< . 1999 Academic Press
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