© 1995 by London Mathematical Society
© The London Mathematical Society
Normal Elements of C*-Algebras of Real Rank Zero without Finite-Spectrum Approximants
Department of Mathematics and Statistics, University of New Mexico Albuquerque, New Mexico 87131, USA
Received 16 December 1992.
We investigate inductive limits of Toeplitz-type C*-algebras. One example, which has real-rank zero, is the middle term of an exact sequence
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is a Bunce-Deddens algebra and I is AF. Using Berg's technique, we produce a normal element N 
that is not the limit of finite-spectrum normals. Moreover, this is an example of a normal element in an inductive limit that is not the limit of normal elements of the approximating subalgebras.
A second example is an embedding of C(
) ( the closed disk) into 
, where is a simple AF algebra and is the Toeplitz algebra. Let n, for n 
2, be the CW complex obtained as the quotient of by an n-fold identification of the boundary. (So 2 = RP2.) Regarding C(n) as a subalgebra of C(), we find nontrivial embeddings of C(n) into type I inductive limits. From this, we produce a *-homomorphism, for n odd, C0(n\{pt}) 
n + 1, that induces an isomorphism on K-theory. More generally, for X a connected CW complex minus a point, and for n odd, we show that the map
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Research partially supported by NSF grant DMS-900734.