On the C*-envelope of approximately finite-dimensional operator algebras
نویسنده
چکیده
The C*-envelope of the limit algebra (or limit space) of a contrac-tive regular system of digraph algebras (or digraph spaces) is shown to be an approximately finite C*-algebra and the direct system for the C*-envelope is determined explicitly.
منابع مشابه
Algebraic orders on K0 and approximately finite operator algebras, J. Operator Th., to appear . 51 S.C. Power, On the outer automorphism groups of triangular alternation limit algebras
Approximately finite (AF) C *-algebras are classified by approximately finite (r-discrete principal) groupoids. Certain natural triangular subalgebras of AF C *-algebras are similarly classified by triangular subsemigroupoids of AF groupoids [10]. Putting this in a more intuitive way, such subalgebras A are classified by the topologised fundamental binary relation R(A) induced on the Gelfand sp...
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An AF C*-algebra has a natural filtration as an increasing sequence of finite dimensional C*-algebras. We show that it is possible to construct a Dirac operator which relates to this filtration in a natural way and which will induce a metric for the weak*-topology on the state space of the algebra. In the particular case of a UHF C*algebra the construction can be made in a way, which relates di...
متن کاملS ep 2 00 3 SPECTRAL TRIPLES FOR AF C * - ALGEBRAS AND METRICS ON THE CANTOR SET
An AF C*-algebra has a natural filtration as an increasing sequence of finite dimensional C*-algebras. We show that it is possible to construct a Dirac operator which relates to this filtration in a natural way and which will induce a metric for the weak*-topology on the state space of the algebra. In the particular case of a UHF C*algebra the construction can be made in a way, which relates di...
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تاریخ انتشار 1995