A simple $C^{\ast }$-algebra with no nontrivial projections
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- by Bruce E. Blackadar PDF
- Proc. Amer. Math. Soc. 78 (1980), 504-508 Request permission
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
- Bruce E. Blackadar, Infinite tensor products of $C^*$-algebras, Pacific J. Math. 72 (1977), no. 2, 313–334. MR 512361, DOI 10.2140/pjm.1977.72.313 —, Traces on simple AF ${C^\ast }$-algebras, J. Functional Anal. (to appear).
- Ola Bratteli, Inductive limits of finite dimensional $C^{\ast }$-algebras, Trans. Amer. Math. Soc. 171 (1972), 195–234. MR 312282, DOI 10.1090/S0002-9947-1972-0312282-2
- Lawrence G. Brown, Philip Green, and Marc A. Rieffel, Stable isomorphism and strong Morita equivalence of $C^*$-algebras, Pacific J. Math. 71 (1977), no. 2, 349–363. MR 463928, DOI 10.2140/pjm.1977.71.349
- John W. Bunce and James A. Deddens, A family of simple $C^{\ast }$-algebras related to weighted shift operators, J. Functional Analysis 19 (1975), 13–24. MR 0365157, DOI 10.1016/0022-1236(75)90003-8
- Jacques Dixmier, Les $C^{\ast }$-algèbres et leurs représentations, Cahiers Scientifiques, Fasc. XXIX, Gauthier-Villars Éditeur, Paris, 1969 (French). Deuxième édition. MR 0246136 —, Simple ${C^\ast }$-algebras, Sympos. on ${C^\ast }$-Algebras (Louisiana State Univ., 1967) (unpublished lecture notes).
- Edward G. Effros and Frank Hahn, Locally compact transformation groups and $C^{\ast }$- algebras, Memoirs of the American Mathematical Society, No. 75, American Mathematical Society, Providence, R.I., 1967. MR 0227310
- Edward G. Effros and Jonathan Rosenberg, $C^{\ast }$-algebras with approximately inner flip, Pacific J. Math. 77 (1978), no. 2, 417–443. MR 510932, DOI 10.2140/pjm.1978.77.417 G. Elliott, On totally ordered groups (to appear).
- James G. Glimm, On a certain class of operator algebras, Trans. Amer. Math. Soc. 95 (1960), 318–340. MR 112057, DOI 10.1090/S0002-9947-1960-0112057-5
- Philip Green, The local structure of twisted covariance algebras, Acta Math. 140 (1978), no. 3-4, 191–250. MR 493349, DOI 10.1007/BF02392308
- Irving Kaplansky, Functional analysis, Some aspects of analysis and probability, Surveys in Applied Mathematics. Vol. 4, John Wiley & Sons, Inc., New York, N.Y.; Chapman & Hall, Ltd., London, 1958, pp. 1–34. MR 0101475
- Shôichirô Sakai, $C^*$-algebras and $W^*$-algebras, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 60, Springer-Verlag, New York-Heidelberg, 1971. MR 0442701 B. Blackadar, A simple unital projectionless ${C^\ast }$-algebra (to appear).
Additional Information
- © Copyright 1980 American Mathematical Society
- 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