Homomorphisms from C(X) into C*-algebras

Canadian Journal of Mathematics

Volumn 49, Issue 5, 1997, Pages 963-1009

  Lin, Huaxin ^a,b  

^a UNIVERSITY OF OREGON   (United States)

^b EAST CHINA NORMAL UNIVERSITY   (China)

Author keywords

Approximation; Classification; Homomorphism of C(S2); Real rank zero

Indexed keywords

EID: 0031371871     PISSN: 0008414X     EISSN: None     Source Type: Journal    
DOI: 10.4153/CJM-1997-050-9     Document Type: Article

References (75)

1. C. A. Akemann and F. Shultz, Perfect C*-algebras. Mem. Amer. Math. Soc. (326) 55(1985).
2. I. D. Berg and K. R. Davidson, Almost commuting matrices and a quantitative version of Brown-Douglas-Fillmore theorem. Acta Math. 166(1991), 121-161.
3. I. D. Berg and C. L. Olsen, A note on almost commuting operators. Proc. Roy. Irish Acad. Sect. A 81(1981), 43-47.
4. B. Blackadar, Notes on the structure of projections in simple C*-algebras. Semesterbericht Funktionalanalysis, Tunbingen, Wintersemester 1982/83.
5. _, K-Theory for Operator Algebras. Springer-Verlag, New York, 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(1991), 211-216.
8. B. Blackadar, A. Kumjian and M. Rørdam, Approximately central matrix units and the structure of noncommutative tori. K-theory 6(1992), 267-284.
9. B. Blackadar and D. Handelman, Dimension functions and traces on C*-algebras. J. Funct. Anal. 48 (1982), 297-340.
10. L. G. Brown, Interpolation by projections in C*-algebras of real rank zero. J. Operator Theory, 26(1991), 383-387.
11. 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.
12. _, Extensions of C*-algebras and K-homology. Ann. of Math. 105(1977), 265-324.
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, Almost commuting matrices need not be nearly commuting. Proc. Amer. Math. Soc. 102 (1988), 529-533.
15. J. Cuntz, The structure of addition and multiplication in simple C*-algebras. Math. Scand. 40(1977), 215-233.
16. _, K-theory for certain C*-algebras. Ann. Math. 131(1981), 181-197.
17. K. R. Davidson, Almost commuting Hermitian matrices. Math. Scand. 56(1985), 222-240.
18. M. Dadarlat and T. A. Loring, The K-theory of abelian subalgebras of AF-algebras. J. Reine Angew. Math. 432(1992), 39-55.
19. J. Dixmier, On some C*-algebras considered by Glimm. J. Funct. Anal. 1(1967), 182-203,
20. 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.
21. E. Effros, Dimensions and C*-algebras. CBMS Regional Conf. Ser. in Math. 46, Amer. Math. Soc., Providence, R.I., 1981.
22. E. Effros, D. Handelman and C.-L. Shen, Dimension groups and their affine representations. Amer. J. Math. 102(1980), 385-407.
23. G. A. Elliott, On the classification of inductive limits of sequences semisimple finite-dimensional algebras. J. Algebra 38(1976), 29-44.
24. _, The classification of C*-algebras of real rank zero. J. Reine Angew. Math. 443(1993), 179-219.
25. _, Dimension groups with torsion. Internat. J. Math 1(1990), 361-380.
26. G. A. Elliott and D. E. Evans, The structure of the irrational rotation C*-algebra. Ann. of Math. 138 (1993), 477-501.
27. G. A. Elliott and G. Gong, On inductive limits of matrix algebras over two-tori. Amer. J. Math. 118(1996), 263-290.
28. _, The classification of C*-algebras of real rank zero II. Ann. of Math. 144(1996), 497-610.
29. G. A. Elliott, G. Gong, H. Lin, and C. Pasnicu, Abelian C*-subalgebras of C*-algebras of real rank zero and inductive limit C*-algebras. Duke Math. J. 85(1996), 511-554.
30. _, Homomorphisms, homotopies and approximation by circle algebras. C. R. Math. Rep. Acad. Sci. Canada (1) 16(1994), 45-50.
31. 2) with prescribed K-theory. J. Funct. Anal. 103(1992), 1-25.
32. R. Exel and T. A. Loring, Almost commuting unitary matrices. Proc. Amer. Math. Soc. 106(1989), 913-915.
33. _, Invariants of almost commuting unitaries. J. Funct. Anal. 95(1991), 364-376.
34. _, An Extension of cellular cohomology to C*-algebras. Trans. Amer. Math. Soc. 392(1992), 141-160.
35. G. Gong and H. Lin, Exponential rank of inductive limit C*-algebras. Math. Scand. 71(1992), 301-319.
36. K. R. Goodearl, Notes on a class of simple C*-algebras with real rank zero. Publ. Mat. 36(1992), 637-654.
37. P. R. Halmos, Some unsolved problems of unknown depth about operators on Hilbert space. Proc. Roy. Soc. Edinburgh Sect. A 76(1976), 67-76.
38. H. E. Jensen, Scattered C*-algebras. Math. Scand. 41(1977), 308-314.
39. H. Lin, Ideals of multiplier algebras of simple AF C*-algebras. Proc. Amer. Math. Soc. 104(1988), 239-244.
40. _, The structure of quasimultipliers of C*-algebras. Trans. Amer. Math. Soc. 315(1989), 147-172.
41. _, Simple C*-algebras with continuous scales and simple corona algebras. Proc. Amer. Math. Soc. 112(1991), 871-880.
42. _, Skeleton C*-subalgebras. Canad. J. Math. 44(1992), 324-343.
43. _, Generalized Weyl-von Neumann theorems. Internat. J. Math. 2(1991), 725-739.
44. _,Generalized Weyl-von Neumann theorems II. Math. Scand. 77(1995), 129-147.
45. _, C*-algebra extensions of C(X). Mem. Amer. Math. Soc. (550) 115(1995).
46. _, Exponential rank of C*-algebras with real rank zero and Brown-Pedersen's conjectures. J. Funct. Anal. 114(1993), 1-11.
47. _, Approximation by normal elements with finite spectra in simple AF-algebras. J. Operator Theory 31(1994), 83-98.
48. _, Approximation by normal elements with finite spectra in C*-algebras of real rank zero. Pacific J. Math. 173(1996), 443-489.
49. _, The generalized Berg theorem and BDF-theorem. Trans. Amer. Math. Soc. 349(1997), 529-545.
50. _, Extensions by C*-algebras of real rank zero II. Proc. London Math. Soc. 71(1995), 641-674.
51. H. Lin, and M. Rørdam, Extensions of inductive limits of circle algebras. J. London Math. Soc. 51(1995), 603-613.
52. H. Lin and S. Zhang, Infinite simple C*-algebras. J. Funct. Anal. 100(1991), 221-231.
53. T. A. Loring, K-theory and asymptotically commuting matrices. Canad. J. Math. 40(1988), 197-216.
54. _, The noncommutative topology of one-dimensional spaces. Pacific J. Math. 136(1989), 145-158.
55. J. Mingo, K-theory and multipliers of stable C*-algebras. Trans. Amer. Math. Soc. 299(1987), 397-412.
56. M. H. A. Newman, Topology of the Plane Sets. Cambridge University Press (1951).
57. C. Pearcy and A. Shields, Almost commuting matrices. J. Funct. Anal. 33(1979), 332-338.
58. G. K. Pedersen, C*-Algebras and their Automorphism Groups. Academic Press, New York, 1979.
59. N. C. Phillips, Simple C*-algebras with property weak (FU). Math. Scand. 69(1991), 127-151.
60. _, Approximation by unitaries with finite spectrum in purely infinite simple C*-algebras. J. Funct. Anal. 120(1994), 98-106.
61. _, Reduction of exponential rank in direct limits of C*-algebras. Canad. J. Math. 46(1994), 818-853.
62. I. Putman, The invertible elements are dense in the irrational rotation C*-algebras. J. Reine Angew. Math. 410(1990), 160-166.
63. M. Rieffel, C*-algebras associated with irrational rotations. Pacific J. Math. 93(1981), 415-429.
64. _, Dimensions and stable rank in the K-theory of C*-algebras. Proc. London Math. Soc. 46(1983), 301-333.
65. _, The cancellation theorem for projective modules over irrational rotation algebras. Proc. London Math. Soc. 47(1983), 258-302.
66. J. J. Schaffer, On unitary dilations of contractions. Proc. Amer. Math. Soc. 6(1955), 322.
67. H. Su, On the classification of C*-algebras of real rank zero: inductive limits of matrix algebras over non-Hausdorff graphs. Mem. Amer. Math. Soc. (114) 547(1995).
68. D. Voiculescu, Remarks on the singular extension in the C*-algebra of the Heisenberg group. J. Operator Theory 5(1981), 147-170.
69. _ Asymptotically commuting finite rank unitaries without commuting approximants. Acta Sci. Math. 451(1983), 429-431.
70. S. Zhang, C*-algebras with real rank zero and the internal structure of their corona and multiplier algebras. Part III. Canad. J. Math. 62(1990), 159-190.
71. _, Certain C*-algebras with real rank zero and their corona and multiplier algebras, Part I. Pacific J. Math. 155(1992), 169-197.
72. _, Certain C*-algebras with real rank zero and their corona and multiplier algebras, Part II. K-theory 6(1992), 1-27.
73. _, Certain C*-algebras with real rank zero and their corona and multiplier algebras, Part IV. Internat. J. Math. 3(1992), 309-330.
74. _, A Riesz decomposition property and ideal structure of multiplier algebras. J. Operator Theory 24(1990), 209-225.
75. _, On the structure of projections and ideals of corona algebras. Canad. J. Math. 61(1989), 721-742.