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Nuclear subalgebras of UHF C*-algebras

Published online by Cambridge University Press:  20 January 2009

R. J. Archbold  and
Alexander Kumjian
R. J. Archbold
Affiliation:
Department of Mathematics, University of California, Santa Barbara, California, 93106, USA
Alexander Kumjian
Affiliation:
School of Mathematics, University of New South Wales, Kensington, N.S.W. 2033, Australia
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A C*-algebra A is said to be approximately finite dimensional (AF) if it is the inductive limit of a sequence of finite dimensional C*-algebras(see [2], [5]). It is said to be nuclear if, for each C*-algebra B, there is a unique C*-norm on the *-algebraic tensor product A ⊗B [11]. Since finite dimensional C*-algebras are nuclear, and inductive limits of nuclear C*-algebras are nuclear [16];,every AF C*-algebra is nuclear. The family of nuclear C*-algebras is a large and well-behaved class (see [12]). The AF C*-algebras for a particularly tractable sub-class which has been completely classified in terms of the invariant K0 [7], [5].

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 29 , Issue 1 , February 1986 , pp. 97 - 100
Copyright
Copyright © Edinburgh Mathematical Society 1986

References

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