Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

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
DOI: https://doi.org/10.1090/S0002-9947-1977-0454648-0
MathSciNet review: 0454648
Full-text PDF

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.


References [Enhancements On Off] (What's this?)

  • [1] O. Bratteli, Inductive limits of finite-dimensional $ {C^\ast}$-algebras, Trans. Amer. Math. Soc. 171 (1972), 195-234. MR 47 #844. MR 0312282 (47:844)
  • [2] J. Dixmier, Les $ {C^\ast}$-algèbres et leurs représentations, Cahiers Scientifiques, no. 29, Gauthier-Villars, Paris, 1964. MR 30 # 1404. MR 0171173 (30:1404)
  • [3] -, On some $ {C^\ast}$-algebras considered by Glimm, J. Functional Analysis 1 (1967), 182-203. MR 35 #4740. MR 0213886 (35:4740)
  • [4] G. A. Elliott, On approximately finite-dimensional von Neumann algebras, Math. Scand. 39 (1976), 91-101. MR 0433222 (55:6200)
  • [5] L. T. Gardner, On the Mackey Borel structure, Canad. J. Math. 23 (1971), 674-678. MR 44 #4532. MR 0287326 (44:4532)
  • [6] J. G. Glimm, Type I $ {C^\ast}$-algebras, Ann. of Math. (2) 73 (1961), 572-612. MR 23 #A2066. MR 0124756 (23:A2066)
  • [7] J. G. Glimm and R. V. Kadison, Unitary operators in $ {C^\ast}$-algebras, Pacific J. Math. 10 (1960), 547-556. MR 22 #5906. MR 0115104 (22:5906)
  • [8] P. R. Halmos, Naive set theory, Van Nostrand, Princeton, N. J., 1960. MR 22 #5575. MR 0114756 (22:5575)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 46L05

Retrieve articles in all journals with MSC: 46L05


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1977-0454648-0
Keywords: Uniqueness of Mackey Borel structure, approximately finite-dimensional $ {C^\ast}$-algebras
Article copyright: © Copyright 1977 American Mathematical Society

American Mathematical Society