The Mackey Borel structure on the spectrum of an approximately finite-dimensional separable 𝐶*-algebra

Elliott, George A.

doi:10.1090/S0002-9947-1977-0454648-0

			Journals Home Search Author Info Subscribe Tech Support My Subscriptions Browser Compatibility Info Help
ISSN 1088-6850(online) ISSN 0002-9947(print)

The Mackey Borel structure on the spectrum of an approximately finite-dimensional separable $C\sp*$ -algebra

Author: George A. Elliott
Journal: Trans. Amer. Math. Soc. 233 (1977), 59-68
MSC: Primary 46L05
MathSciNet review: 0454648
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: It is shown that the Mackey Borel structures on the spectra of any two approximately finite-dimensional separable ${C^\ast}$ -algebras not of type I are isomorphic.

[1] Ola Bratteli, Inductive limits of finite dimensional 𝐶*-algebras, Trans. Amer. Math. Soc. 171 (1972), 195–234. MR 0312282 (47 #844), http://dx.doi.org/10.1090/S0002-9947-1972-0312282-2
[2] Jacques Dixmier, Les 𝐶*-algèbres et leurs représentations, Cahiers Scientifiques, Fasc. XXIX, Gauthier-Villars & Cie, Éditeur-Imprimeur, Paris, 1964 (French). MR 0171173 (30 #1404)
[3] J. Dixmier, On some 𝐶*-algebras considered by Glimm, J. Functional Analysis 1 (1967), 182–203. MR 0213886 (35 #4740)
[4] George A. Elliott, On approximately finite-dimensional von Neumann algebras, Math. Scand. 39 (1976), no. 1, 91–101. MR 0433222 (55 #6200)
[5] L. Terrell Gardner, On the Mackey Borel structure, Canad. J. Math. 23 (1971), 674–678. MR 0287326 (44 #4532)
[6] James Glimm, Type I 𝐶*-algebras, Ann. of Math. (2) 73 (1961), 572–612. MR 0124756 (23 #A2066)
[7] James G. Glimm and Richard V. Kadison, Unitary operators in 𝐶*-algebras, Pacific J. Math. 10 (1960), 547–556. MR 0115104 (22 #5906)
[8] Paul R. Halmos, Naive set theory, The University Series in Undergraduate Mathematics, D. Van Nostrand Co., Princeton, N.J.-Toronto-London-New York, 1960. MR 0114756 (22 #5575)

	Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
\|

Bibliography