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

HTML articles powered by AMS MathViewer

- 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
—, - 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**
—, - 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, - 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,

*Traces on simple AF*${C^\ast }$-

*algebras*, J. Functional Anal. (to appear).

*Simple*${C^\ast }$-

*algebras*, Sympos. on ${C^\ast }$-Algebras (Louisiana State Univ., 1967) (unpublished lecture notes).

*On totally ordered groups*(to appear).

*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