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On the Approximation of Quasidiagonal C*-Algebras

โœ Scribed by Marius Dadarlat

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
118 KB
Volume
167
Category
Article
ISSN
0022-1236

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โœฆ Synopsis

Let A be a separable exact quasidiagonal C*-algebra. Suppose that ?: A ร„ L(H) is a faithful representation whose image does not contain nonzero compact operators. Then there exists a sequence . n : A ร„ L(H) of completely positive contractions such that &?(a)&. n (a)& ร„ 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=D 1 ร„ D 2 ร„ } } } with sup i rank(D i )< .

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