On the stable rank of simple C*-algebras

Journal of the American Mathematical Society

Volumn 12, Issue 4, 1999, Pages 1091-1102

  Villadsen, Jesper ^a,b  

^a AARHUS UNIVERSITY   (Denmark)

^b UNIVERSITY OF SOUTHERN DENMARK   (Denmark)

Author keywords

Nonstable K theory; Real rank; Simple C* algebra; Stable rank

Indexed keywords

EID: 0033450072     PISSN: 08940347     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0894-0347-99-00314-8     Document Type: Article

References (20)

1. Beggs, E. J. and Evans, D. E., The real rank of algebras of matrix valued functions, Internat. J. Math., 2, (1991), pp. 131-138. MR 92e:46114
2. Blackadar, B., A stable cancellation theorem tor simple C*-algebras, Proc. London Math. Soc., (3), 47, (1983), pp. 303-305. MR 85g:46086
3. Blackadar, B., Comparison theory for simple C*-algebras, Operator Algebras and Applications, L.M.S. Lecture Notes Series, 135, (1989), pp. 21-54. MR 90g:46078
4. Blackadar, B., Dǎdǎrlat, M., and Roørdam, M., The real rank of inductive limit C*-algebras, Math. Scand, 69, (1991), pp. 211-216. MR 93e:46067
5. Blackadar, B., Kumjian, A. and Røordam, M., Approximately central matrix units and the structure of noncommutative tori, K-theory, 6, (1992), pp. 267-284. MR 93i:46129
6. Brown, L. and Pedersen, G. K., C* algebras of real rank zero, J. Funct. Anal., 99, (1991). pp. 131-149. MR 92m:46086
7. Cuntz, J., K-theory for certain C*-algebras, Ann. of Math., 113, (1981), pp. 181-197. MR 84c:46058
8. Dǎdǎrlat, M., Nagy. G., Némethi, A. and Pasnicu, C., Reduction of topological stable rank in inductive limits of C*-algebras , Pacific J. Math., 153, (1992), pp. 267-276. MR 93d:46119
9. Dold, A., Lectures on Algebraic Topology, Springer Verlag, 1972. MR 54:3685 -
10. Fell, J. M. G., The structure of algebras of operator fields, Acta. math., 106, (1961), pp. 233-280. MR 29:15
11. Guillemin, V. and Pollack, A., Differential topology, Prentice-Hall, New Jersey, 1974. MR 50:1276
12. Herman, R. H. and Vaserstein, L. N., The stable range of C*-algebras, Invent. math., 77, (1984), pp. 553-555. MR 86a:46074
13. Husemoller, D., Fibre Bundles, McGraw-Hill, New York, 1966. MR 37:4821
14. Milnor, J. W. and Stasheff, J. D., Characteristic Classes, Annals of Mathematics Studies, No.76, Princeton University Press, 1974. MR 55:13428
15. Nistor, V., Stable rank for a certain class of type I C*-algebras, J. Operator Theory, 17, (1987), pp. 365-373. MR 88h:46110
16. Rieffel, M. A., Dimension and stable rank in the K-theory of C*-algebras, Proc. London Math. Soc. (3), 46, (1983), pp. 301-333. MR 84g:46085
17. Rieffel, M. A., The cancellation theorem for projective modules over irrational rotation C*-algebras, Proc. London Math. Soc. (3), 47, (1983), pp. 285-302. MR 85g:46085
18. Rieffel, M. A., The homotopy groups of the unitary groups of non-commutative tori, J. Operator Theory, 17, (1987), pp. 237-254. MR 88f:22018
19. Roørdam, M., On the structure of simple C*-algebras tensored with a UHF-algebra, J. Funct. Anal., 100, (1991), pp. 1-17. MR 92m:46091
20. Villadsen, J., Simple C*-algebras with perforation, J. Funct. Anal., 154, (1998), pp. 110 116. CMP 98:11