caa a22 4500 397532644 CHVBK 20180308164655.0 cr unu---uuuuu 161202e199504 xx s 000 0 eng 10.1112/jlms/51.2.353 doi (NATIONALLICENCE)oxford-10.1112/jlms/51.2.353 Loring Terry A. Department of Mathematics and Statistics, University of New Mexico Albuquerque, New Mexico 87131, USA Normal Elements of C*-Algebras of Real Rank Zero without Finite-Spectrum Approximants [Elektronische Daten] [Terry A. Loring] We investigate inductive limits of Toeplitz-type C*-algebras. One example, which has real-rank zero, is the middle term of an exact sequence 0→I→𝒜→πB→0, where ℬ is a Bunce-Deddens algebra and I is AF. Using Berg's technique, we produce a normal element N ∈ 𝒜 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(𝔻) (𝔻 the closed disk) into 𝒜 ⊗ 𝒯, where 𝒜 is a simple AF algebra and 𝒯 is the Toeplitz algebra. Let 𝔻n, for n ≥ 2, be the CW complex obtained as the quotient of 𝔻 by an n-fold identification of the boundary. (So 𝔻2 = RP2.) Regarding C(𝔻n) as a subalgebra of C(𝔻), we find nontrivial embeddings of C(𝔻n) into type I inductive limits. From this, we produce a *-homomorphism, for n odd, C0(𝔻n\{pt}) → 𝒪n + 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[C0(X),𝒪n+1] → KK(C0(X),𝒪n+1)is a split surjection. © The London Mathematical Society Notes and Papers nationallicence Journal of the London Mathematical Society Oxford University Press 51/2(1995-04), 353-364 0024-6107 51:2<353 1995 51 jlms https://doi.org/10.1112/jlms/51.2.353 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1112/jlms/51.2.353 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Loring Terry A. Department of Mathematics and Statistics, University of New Mexico Albuquerque, New Mexico 87131, USA NATIONALLICENCE 773 0- Journal of the London Mathematical Society Oxford University Press 51/2(1995-04), 353-364 0024-6107 51:2<353 1995 51 jlms Metadata rights reserved CC BY-NC-4.0 http://creativecommons.org/licenses/by-nc/4.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-oxford