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A simple $ C\sp{\ast} $-algebra with no nontrivial projections


Author: Bruce E. Blackadar
Journal: Proc. Amer. Math. Soc. 78 (1980), 504-508
MSC: Primary 46L05
DOI: https://doi.org/10.1090/S0002-9939-1980-0556621-6
MathSciNet review: 556621
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Abstract: A $ {C^\ast}$-algebra is constructed which is separable, simple, nuclear, non-unital, and contains no nonzero projections. Some results on automorphisms of AF algebras are also obtained.


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

  • [1] B. Blackadar, Infinite tensor products of $ {C^\ast}$-algebras, Pacific J. Math. 72 (1977), 313-334. MR 0512361 (58:23622)
  • [2] -, Traces on simple AF $ {C^\ast}$-algebras, J. Functional Anal. (to appear).
  • [3] O. Bratteli, Inductive limits of finite-dimensional $ {C^\ast}$-algebras, Trans. Amer. Math. Soc. 171 (1972), 195-234. MR 0312282 (47:844)
  • [4] L. Brown, P. Green and M. Rieffel, Stable isomorphism and strong Morita equivalence of $ {C^\ast}$-algebras, Pacific J. Math. 71 (1977), 349-364. MR 0463928 (57:3866)
  • [5] J. Bunce and J. Deddens, A family of simple $ {C^\ast}$-algebras related to weighted shift operators, J. Functional Analysis 19 (1975), 13-24. MR 0365157 (51:1410)
  • [6] J. Dixmier, Les $ {C^\ast}$-algèbres et leurs représentations, Gauthier-Villars, Paris, 1969. MR 0246136 (39:7442)
  • [7] -, Simple $ {C^\ast}$-algebras, Sympos. on $ {C^\ast}$-Algebras (Louisiana State Univ., 1967) (unpublished lecture notes).
  • [8] E. Effros and F. Hahn, Locally compact transformation groups and $ {C^\ast}$-algebras, Mem. Amer. Math. Soc. No. 75 (1967). MR 0227310 (37:2895)
  • [9] E. Effros and J. Rosenberg, $ {C^\ast}$-algebras with approximately inner flip, Pacific J. Math. 77 (1978), 417-443. MR 510932 (80k:46065)
  • [10] G. Elliott, On totally ordered groups (to appear).
  • [11] J. Glimm, On a certain class of operator algebras, Trans. Amer. Math. Soc. 95 (1960), 318-340. MR 0112057 (22:2915)
  • [12] P. Green, The local structure of twisted covariance algebras, Acta Math. 140 (1978), 191-250. MR 0493349 (58:12376)
  • [13] I. Kaplansky, Functional analysis, some aspects of analysis and probability, Wiley, New York, 1958, pp. 1-34. MR 0101475 (21:286)
  • [14] S. Sakai, $ {C^\ast}$-algebras and $ {W^\ast}$-algebras, Springer-Verlag, Berlin and New York, 1971. MR 0442701 (56:1082)
  • [15] B. Blackadar, A simple unital projectionless $ {C^\ast}$-algebra (to appear).

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DOI: https://doi.org/10.1090/S0002-9939-1980-0556621-6
Article copyright: © Copyright 1980 American Mathematical Society

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