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Subquotients of UHF C*-algebras

Published online by Cambridge University Press:  24 October 2008

Simon Wassermann
Simon Wassermann
Affiliation:
Department of Mathematics, University of Glasgow, Glasgow G12 9XF, U.K.
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Extract

Over the last thirty years, the study of C*-algebras has proceeded in a number of directions. On one hand, much effort has been devoted to understanding the structure of particular classes of algebras, such as the approximately finite (AF) algebras. On the other, general structure theorems have been sought. Classes of algebras defined by certain abstract properties have been investigated with a view to obtaining more concrete descriptions of the algebras. One of the earliest results of this type was the theorem of Glimm [13], later extended by Sakai [20] to the inseparable case, characterizing the non-type I C*-algebras as those algebras which contain a subalgebra with a quotient *-isomorphic to the CAR algebra.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 115 , Issue 3 , May 1994 , pp. 489 - 500
Copyright
Copyright © Cambridge Philosophical Society 1994

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References

REFERENCES

[1]Archbold, R. J. and Batty, C. J. K.. C*-tensor norms and slice maps. J. London Math. Soc. 22 (1980), 127–138.CrossRefGoogle Scholar
[2]Arveson, W.. Notes on extensions of C*-algebras. Duke Math. J. 44 (1977), 329–355.CrossRefGoogle Scholar
[3]Brown, L. G.. Semicontinuity and multipliers of C*-algebras. Can. J. Math. 40 (1988), 865–988.CrossRefGoogle Scholar
[4]Choi, M. D.. A Schwarz inequality for positive linear maps on C*-algebras. Ill. J. Math. 18 (1974), 565–574.Google Scholar
[5]Choi, M. D.. A simple C*-algebra generated by two finite-order unitaries. Can. J. Math. 31 (1979), 887–890.CrossRefGoogle Scholar
[6]Choi, M. D. and Effros, E. G.. Nuclear C*-algebras and the approximation property. Amer. J. Math. 100 (1978), 61–79.CrossRefGoogle Scholar
[7]Choi, M. D. and Effros, E. G.. Separable nuclear C*-algebras and injectivity. Duke Math. J. 43 (1976), 309–322.CrossRefGoogle Scholar
[8]Choi, M. D. and Eferos, E. G.. Nuclear C*-algebras and injectivity: the general case. Indiana Univ. Math. J. 26 (1977), 443–446.CrossRefGoogle Scholar
[9]Choi, M. D. and Effros, E. G.. The completely positive lifting problem for C*-algebras. Ann. Math. 104 (1976), 585–609.CrossRefGoogle Scholar
[10]Connes, A.. A classification of injective factors. Ann. Math. 104 (1976), 73–116.CrossRefGoogle Scholar
[11]Effros, E. C. and Haagerup, U.. Lifting problems and local reflexivity for C*-algebras. Duke Math. J. 52 (1985), 103–128.CrossRefGoogle Scholar
[12]Elliott, G.. Automorphisms determined by multipliers on ideals of a C*-algebra. J. Functional Analysis 23 (1976), 1–10.CrossRefGoogle Scholar
[13]Glimm, J.. Type I C*-algebras. Ann. Math. 73 (1961), 572–612.CrossRefGoogle Scholar
[14]Kirchberg, E.. C*-nuclearity implies CPAP. Math. Nachr. 76 (1977), 203–212.CrossRefGoogle Scholar
[15]Kirchberg, E.. The Fubini theorem for exact C*-algebras. J. Operator Theory 10 (1983), 3–8.Google Scholar
[16]Kirchberg, E.. On restricted perturbations in inverse images and a description of normalizer algebras in C*-algebras. J. Functional Analysis (to appear).Google Scholar
[17]Kirchberg, E.. On subalgebras of the CAR-algebra, J. Functional Analysis (to appear).Google Scholar
[18]Lance, E. C.. On nuclear C*-algebras. J. Functional Analysis 12 (1973), 157–176.CrossRefGoogle Scholar
[19]Paulsen, V.. Completely bounded maps and dilations. Pitman Research Notes in Mathematics no. 146, Longman (1986).Google Scholar
[20]Sakai, S.. A characterisation of type I C*-algebras. Bull. Amer. Math. Soc. 72 (1966), 508–512.CrossRefGoogle Scholar
[21]Stinespring, W. F.. Positive functions on C*-algebras. Proc. A.M.S. 9 (1955), 211–216.Google Scholar
[22]Takesaki, M.. On the cross-norm of the direct product of C*-algebras. Tôhoku Math. J. 15 (1964), 111–122.Google Scholar
[23]Wassermann, S.. On tensor products of certain group C*-algebras. J. Functional Analysis 23 (1976), 239–254.CrossRefGoogle Scholar
[24]Wassermann, S.. Injective W*-algebras. Math. Proc. Cambridge Phil. Soc. 82 (1977), 39–47.CrossRefGoogle Scholar
[25]Wassermann, S.. Tensor products of free-group C*-algebras. Bull. London Math. Soc. 22 (1990), 375–380.CrossRefGoogle Scholar
[26]Wassermann, S.. C*-algebras associated with groups with Kazhdan's property T. Ann. Math. 134 (1991), 423–431.CrossRefGoogle Scholar