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)



AF algebras with directed sets of finite-dimensional $ \sp{\ast} $-subalgebras

Author: Aldo J. Lazar
Journal: Trans. Amer. Math. Soc. 275 (1983), 709-721
MSC: Primary 46L35; Secondary 46L45
MathSciNet review: 682726
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We characterize the unital $ AF$ algebras whose families of finite dimensional $ ^{\ast}$-subalgebras are directed by inclusion. A representation theorem for the algebras of this class allows us to classify them up to $ ^{\ast} $-isomorphisms.

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

  • [1] O. Bratelli, Inductive limits of finite dimensional $ {C^{\ast} }$-algebras, Trans. Amer. Math. Soc. 171 (1972), 195-234. MR 0312282 (47:844)
  • [2] O. Bratelli and G. A. Elliott, Structure spaces of approximately finite-dimensional $ {C^{\ast} }$-algebras. II, J. Funct. Anal. 30 (1978), 74-82. MR 513479 (80d:46111)
  • [3] J. Dixmier, Les $ {C^{\ast} }$-algèbres et leur représentations, Gauthier-Villars, Paris, 1969.
  • [4] J. M. G. Fell, The structure of algebras of operator fields, Acta Math. 106 (1961), 233-280. MR 0164248 (29:1547)
  • [5] J. G. Glimm, On a certain class of operator algebras, Trans. Amer. Math. Soc. 95 (1960), 318-340. MR 0112057 (22:2915)
  • [6] K. H. Hofmann and F. J. Thayer, Approximately finite dimensional $ {C^{\ast} }$-algebras, Dissertationes Math. (Rozprawy Mat.) 174 (1980), 64 pp. MR 576994 (81h:46072)
  • [7] A. J. Lazar, On some elementary properties of $ AF$ algebras, Indiana Univ. Math. J. 30 (1981), 433-439. MR 611231 (82j:46075)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 46L35, 46L45

Retrieve articles in all journals with MSC: 46L35, 46L45

Additional Information

Article copyright: © Copyright 1983 American Mathematical Society

American Mathematical Society