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Subquotients of UHF \(C^*\)-algebras. (English) Zbl 0824.46069
Let \(B\) be a UHF \(C^*\)-algebra. In [J. Funct. Analysis 129, 1-34, 35-63 (1995)], E. Kirchberg has shown that in order for a \(C^*\)-algebra \(A\) to be exact, it is necessary and sufficient that \(A\) be isomorphic to some quotient of a \(C^*\)-subalgebra of \(B\).
In the present paper, the author provides a simplified and relatively self-contained exposition of the proof.

MSC:
46L35 Classifications of \(C^*\)-algebras
46L05 General theory of \(C^*\)-algebras
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References:
[1] DOI: 10.1112/jlms/s2-22.1.127 · Zbl 0437.46049 · doi:10.1112/jlms/s2-22.1.127
[2] DOI: 10.1215/S0012-7094-77-04414-3 · Zbl 0368.46052 · doi:10.1215/S0012-7094-77-04414-3
[3] DOI: 10.1016/0022-1236(73)90021-9 · Zbl 0252.46065 · doi:10.1016/0022-1236(73)90021-9
[4] Kirchberg, J. Functional Analysis
[5] Kirchberg, J. Functional Analysis
[6] Kirchberg, J. Operator Theory 10 pp 3– (1983)
[7] DOI: 10.1002/mana.19770760115 · Zbl 0383.46011 · doi:10.1002/mana.19770760115
[8] DOI: 10.2307/1970319 · Zbl 0152.33002 · doi:10.2307/1970319
[9] DOI: 10.1016/0022-1236(76)90054-9 · Zbl 0335.46037 · doi:10.1016/0022-1236(76)90054-9
[10] DOI: 10.1215/S0012-7094-85-05207-X · Zbl 0613.46047 · doi:10.1215/S0012-7094-85-05207-X
[11] DOI: 10.2307/1971057 · Zbl 0343.46042 · doi:10.2307/1971057
[12] DOI: 10.2307/2944351 · Zbl 0754.46040 · doi:10.2307/2944351
[13] DOI: 10.1112/blms/22.4.375 · Zbl 0717.46049 · doi:10.1112/blms/22.4.375
[14] Wassermann, Math. Proc. Cambridge Phil. Soc 82 pp 39– (1977)
[15] DOI: 10.1016/0022-1236(76)90050-1 · Zbl 0358.46040 · doi:10.1016/0022-1236(76)90050-1
[16] DOI: 10.2748/tmj/1178243737 · Zbl 0127.07302 · doi:10.2748/tmj/1178243737
[17] DOI: 10.2307/2032342 · Zbl 0064.36703 · doi:10.2307/2032342
[18] DOI: 10.1090/S0002-9904-1966-11520-3 · Zbl 0141.12305 · doi:10.1090/S0002-9904-1966-11520-3
[19] DOI: 10.2307/1970968 · Zbl 0361.46067 · doi:10.2307/1970968
[20] DOI: 10.1512/iumj.1977.26.26034 · Zbl 0378.46052 · doi:10.1512/iumj.1977.26.26034
[21] DOI: 10.1215/S0012-7094-76-04328-3 · Zbl 0382.46026 · doi:10.1215/S0012-7094-76-04328-3
[22] DOI: 10.2307/2373876 · Zbl 0397.46054 · doi:10.2307/2373876
[23] Choi, Can. J. Math 31 pp 887– (1979) · Zbl 0441.46047 · doi:10.4153/CJM-1979-082-4
[24] Choi, Ill. J. Math 18 pp 565– (1974)
[25] Brown, Can. J. Math 40 pp 865– (1988) · Zbl 0647.46044 · doi:10.4153/CJM-1988-038-5
[26] Paulsen, Completely bounded maps and dilations (1986) · Zbl 0614.47006
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