Approximation by normal elements with finite spectra in C*-algebras of real rank zero

Pacific Journal of Mathematics

Volumn 173, Issue 2, 1996, Pages 443-489

  Lin, Huaxin ^a  

^a UNIVERSITY OF OREGON   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000604532     PISSN: 00308730     EISSN: None     Source Type: Journal    
DOI: 10.2140/pjm.1996.173.443     Document Type: Article

References (51)

1. E.M. Alfsen, Compact Convex Sets and Bounded Integrals, Springer-Verlag, Berlin, Heidelberg, New York, 1971.
2. I.D. Berg and K. Davidson, Almost commuting matrices and a quantitive version of Brown-Douglas-Fillmore theorem, Acta Math., 166 (1991), 121-161.
3. B. Blackadar, Notes on the structure of projections in simple C* -algebras, Semester-bericht Funktionalanalysis, Tunbingen, Wintersemester 1982/83.
4. _, Traces on simple AF-algebras, J. Funct. Anal., 38 (1980), 156-168.
5. _, K-Theory for Operator Algebras, Springer-Verlag, New York, Berlin, Heidelberg, London, Paris, Tokyo 1986.
6. B. Blackadar, O. Bratteli, G.A. Elliott, and A. Kumjian, Reduction of real rank in inductive limits of C* -algebras, Math. Ann., 292 (1992), 111-126.
7. B. Blackadar, M. Dadarlat and M. Rørdam, The real rank of inductive limit C* -algebras, Math. Scand., 69 (1992), 211-216.
8. B. Blackadar, K. Kumjian, and M. Rørdam, Approximately central matrix units and the structure of noncommutative tori, K-theory, 6 (1992), 267-284.
9. O. Bratteli, Inductive limits of finite dimensional C* -algebras, Trans. Amer. Math. Soc., 17 (1972), 195-234.
10. L.G. Brown, Stable isomorphism of hereditary subalgebras of C* -algebras, Pacific J. Math., 71 (1977), 195-234.
11. _, Interpolation by projections in C* -algebras of real rank zero, preprint.
12. L.G. Brown, R. Douglas and P. Fillmore, Unitary equivalence modulo the compact operators and extensions of C* -algebras, Proc. Conf. on Operator Theory, Springer Lecture Notes in Math., 345 (1973), 58-128.
13. L.G. Brown and G.K. Pedersen, C* -algebras of real rank zero, J. Funct. Anal., 99 (1991), 131-149.
14. M.-D. Choi, Lifting projections from quotient C* -algebras, J. Operator Theory, 10 (1983), 21-30.
15. M.-D. Choi and G. A. Elloitt, Density of the selfadjoint elements with finite spectrum in an irrational rotation C* -algebra, Math. Scand., 67 (1990), 73-86.
16. J. Cuntz, K-theory for certain C* -algebras, Ann. Math., 131 (1981), 181-197.
17. K. Davidson, Almost commuting Hermitian matrices, Math. Scand., 56 (1985), 222-240.
18. J. Dixmier, On some C* -algebras considered by Glimm, J. Functional Analysis, I (1967), 182-203.
19. M. Dadarlat, G. Nagy, A. Nemethi and C. Pasnicu, Reduction of topological stable rank in inductive limits of C* -algebras, Pacific J. Math., 153 (1992), 267-276.
20. E. Efrros, Dimensions and C* -algebras, CBMS Reginal. Conf. Ser. in Math., no. 46, Amer. Math. Soc., Providence, R.I., 1981.
21. E. Efrros, D. Handelman and C.-L Shen, Dimension groups and their affine representations, Amer. J. Math., 102 (1980), 385-407.
22. G. A. Elliott, On the classification of inductive limits of sequences semisimple finite-dimensinal algebras, J. Algebra, 38 (1976), 29-44.
23. _, The classification of C* -algebras of real rank zero, J. reine angew. Math., 443 (1993), 179-219.
24. G.A. Elliott and D.E. Evans, The structure, of the irrational rotation C* -algebra, Ann. Math., 138 (1993), 477-501.
25. H. Freudenthal, Entwicklungen von Raumen und ihren Gruppen, Compositio Math., 4 (1937), 145-234.
26. K.R. Goodearl, Notes on a class of simple C* -algebras with real rank zero, Publications Mate., 36 (1992), 637-654.
27. _, Partially Ordered Abelian Groups with Interpolation, Math. Surveys and Monographs 20, Amer. Math. Soc., Providence, 1986.
28. G. Gong and H. Lin, Exponential rank of inductive limit C* -algebras, Math. Scand., 71 (1992), 301-319.
29. H. Lin, Ideals of multiplier algebras of simple AF C* -algebras, Proc. Amer. Math. Soc., 104 (1988), 239-244.
30. _, Generalized Weyl-von Neumann theorems, International J. Math., 2 (1991), 725-739.
31. _, Generalized Weyl-von Neumann theorems (II), Math. Scand., to appear.
32. _, C* -algebra Extensions of C(X), Memoirs Amer. Math. Soc., 115 (1995), no.550.
33. _, Exponential rank of C* -algebras with real rank zero and Brown-Pedersen's conjecture, J. Funct. Anal., 114 (1993), 1-11.
34. _, Approximation by normal elements with finite spectra in simple AF-algebras, J. Operator theory, 31 (1994), 83-98.
35. _, Simple C* -algebras with continuous scales and simple corona algebras, Proc. Amer. Math. Soc., 112 (1991), 871-880.
36. H. Lin and S. Zhang, Infinite simple C* -algebras, J. Funct. Anal., 100 (1991), 221-231.
37. N.C. Phillips, Simple C* -algebras with property weak (FU), Math. Scand., 69 (1991), 127-151.
38. _, Approximation by unitaries with finite spectrum in purely infinite simple C* -algebras, J. Func. Anal., 120 (1994), 98-106.
39. I. Putman, The invertible elements are dense in the irrational rotation C* -algebras, J. Reine Angew. Math., 410 (1990), 160-166.
40. M. Rieffel, C* -algebras associated with irrational rotation, Pacific J. Math., 93 (1981), 415-429.
41. _, The cancellation theorem for projectile modules over irrational rotation algebras, Proc. London Math. Soc., 46(3) (1983), 301-333.
42. S. Sakai, C* -algebras and W* -algebras, Springer-verlag, New York/Berlin, 1971.
43. H. Su, On the classification of C* -algebras of real rank zero: inductive limits of matrix algebras over non-Hausdorff graphs, preprint.
44. D. Voiculescu, Remarks on the singular extension in the C* -algebra of the Heisenberg group, J. Operator Theory, 5 (1981), 147-170.
45. _, Asymptotically commuting finite rank unitaries without commuting approximants, Acta. Sci. Math., 451 (1983), 429-431.
46. S. Zhang, C* -algebras with real rank zero and the internal structure of their corona and multiplier algebras, Part III, Can. J. Math., 62 (1990), 159-190.
47. _, Certain C* -algebras with real rank zero and their corona and multiplier algebras, Part I, Pacific J. Math., 155 (1992), 169-197.
48. _, Certain C* -algebras with real rank zero and their corona and multiplier algebras, Part II, K-theory, 6 (1992), 1-27.
49. _, Certain C* -algebras with real rank zero and their corona and multiplier algebras, International J. Math., 3 (1992), 309-330.
50. _, A Riesz decomposition property and ideal structure of multiplier algebras, J. Operator Theory, 24 (1990), 209-225.
51. _, On the structure of projections and ideals of corona algebras, Can. J. Math., 61 (1989), 721-742.