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Abelian \mathrm{C}^\ast-subalgebras of \mathrm{C}^\ast-algebras of real rank zero and inductive limit \mathrm{C}^\ast-algebras

George A. Elliott, Guihua Gong, Huaxin Lin, and Cornel Pasnicu
Source: Duke Math. J. Volume 85, Number 3 (1996), 511-554.
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Primary Subjects: 46L35
Secondary Subjects: 46L45, 46L80
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Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077243441
Mathematical Reviews number (MathSciNet): MR1422356
Zentralblatt MATH identifier: 0869.46030
Digital Object Identifier: doi:10.1215/S0012-7094-96-08520-8

References

[Al] E. M. Alfsen, Compact convex sets and boundary integrals, Ergebnisse der Mathematik und ihrer Grenzgebiete, vol. 57, Springer-Verlag, New York, 1971.
Mathematical Reviews (MathSciNet): MR56:3615
Zentralblatt MATH: 0209.42601
[BD] I. D. Berg and K. Davidson, Almost commuting matrices and a quantitative version of the Brown-Douglas-Fillmore theorem, Acta Math. 166 (1991), no. 1-2, 121–161.
Mathematical Reviews (MathSciNet): MR92f:47015
Zentralblatt MATH: 0731.47009
Digital Object Identifier: doi:10.1007/BF02398885
[Bl1] B. Blackadar, Notes on the structure of projections in simple $C^\ast$-algebras, unpublished, Semesterbericht Funktionalanalysis, Tübingen, Wintersemester, 1982–83, 93–137.
[Bl2] B. Blackadar, Traces on simple AF $C\sp\ast$-algebras, J. Funct. Anal. 38 (1980), no. 2, 156–168.
Mathematical Reviews (MathSciNet): MR82a:46062
Zentralblatt MATH: 0443.46037
Digital Object Identifier: doi:10.1016/0022-1236(80)90062-2
[Bl3] B. Blackadar, $K$-theory for operator algebras, Mathematical Sciences Research Institute Publications, vol. 5, Springer-Verlag, New York, 1986.
Mathematical Reviews (MathSciNet): MR88g:46082
Zentralblatt MATH: 0597.46072
[BBEK] B. Blackadar, O. Bratteli, G. A. Elliott, and A. Kumjian, Reduction of real rank in inductive limits of $C\sp \ast$-algebras, Math. Ann. 292 (1992), no. 1, 111–126.
Mathematical Reviews (MathSciNet): MR93a:46112
Zentralblatt MATH: 0738.46027
Digital Object Identifier: doi:10.1007/BF01444612
[BDR] B. Blackadar, M. Dadarlat, and M. Rørdam, The real rank of inductive limit $C\sp\ast$-algebras, Math. Scand. 69 (1991), no. 2, 211–216 (1992).
Mathematical Reviews (MathSciNet): MR93e:46067
Zentralblatt MATH: 0776.46025
[BKR] B. Blackadar, A. Kumjian, and M. Rørdam, Approximately central matrix units and the structure of noncommutative tori, $K$-Theory 6 (1992), no. 3, 267–284.
Mathematical Reviews (MathSciNet): MR93i:46129
Zentralblatt MATH: 0813.46064
Digital Object Identifier: doi:10.1007/BF00961466
[Bo] R. Bott, Lectures on $K(X)$, Mathematics Lecture Note Series, W. A. Benjamin, Inc., New York-Amsterdam, 1969.
Mathematical Reviews (MathSciNet): MR41:2667
Zentralblatt MATH: 0194.23904
[Br] O. Bratteli, Inductive limits of finite dimensional $C\sp\ast$-algebras, Trans. Amer. Math. Soc. 171 (1972), 195–234.
Mathematical Reviews (MathSciNet): MR47:844
Zentralblatt MATH: 0264.46057
Digital Object Identifier: doi:10.2307/1996380
[BE] O. Bratteli and G. A. Elliott, Small eigenvalue variation and real rank zero, to appear in Pacific J. Math. 174, 1996.
Mathematical Reviews (MathSciNet): MR1419472
Zentralblatt MATH: 0865.46039
Project Euclid: euclid.pjm/1102364181
[Bn] L. G. Brown, Interpolation by projections in $C\sp\ast$-algebras of real rank zero, J. Operator Theory 26 (1991), no. 2, 383–387.
Mathematical Reviews (MathSciNet): MR94j:46054
Zentralblatt MATH: 0808.46082
[BDF] L. G. Brown, R. G. Douglas, and P. A. Fillmore, Unitary equivalence modulo the compact operators and extensions of $C\sp\ast$-algebras, Proceedings of a Conference on Operator Theory (Dalhousie Univ., Halifax, N.S., 1973), Springer-Verkag, Berlin,New York, 1973, 58–128. Lecture Notes in Math., Vol. 345.
Mathematical Reviews (MathSciNet): MR52:1378
Zentralblatt MATH: 0277.46053
[BP] L. G. Brown and G. K. Pedersen, $C\sp\ast$-algebras of real rank zero, J. Funct. Anal. 99 (1991), no. 1, 131–149.
Mathematical Reviews (MathSciNet): MR92m:46086
Zentralblatt MATH: 0776.46026
Digital Object Identifier: doi:10.1016/0022-1236(91)90056-B
[Ch] M.-D. Choi, Lifting projections from quotient $C\sp\ast$-algebras, J. Operator Theory 10 (1983), no. 1, 21–30.
Mathematical Reviews (MathSciNet): MR85c:46060
Zentralblatt MATH: 0538.46041
[CE] M.-D. Choi and G. A. Elliott, Density of the selfadjoint elements with finite spectrum in an irrational rotation $C\sp\ast$-algebra, Math. Scand. 67 (1990), no. 1, 73–86.
Mathematical Reviews (MathSciNet): MR92a:46062
Zentralblatt MATH: 0743.46070
[Cu] J. Cuntz, $K$-theory for certain $C\sp\ast$-algebras, Ann. of Math. (2) 113 (1981), no. 1, 181–197.
Mathematical Reviews (MathSciNet): MR84c:46058
Zentralblatt MATH: 0437.46060
Digital Object Identifier: doi:10.2307/1971137
[DN] M. Dadarlat and A. Nemethi, Shape theory and (connective) $K$-theory, J. Operator Theory 23 (1990), no. 2, 207–291.
Mathematical Reviews (MathSciNet): MR91j:46092
Zentralblatt MATH: 0755.46036
[D] K. Davidson, Almost commuting Hermitian matrices, Math. Scand. 56 (1985), no. 2, 222–240.
Mathematical Reviews (MathSciNet): MR87e:47012
Zentralblatt MATH: 0563.15010
[Dix] J. Dixmier, On some $C\sp\ast$-algebras considered by Glimm, J. Funct. Anal. 1 (1967), 182–203.
Mathematical Reviews (MathSciNet): MR35:4740
Zentralblatt MATH: 0152.33003
Digital Object Identifier: doi:10.1016/0022-1236(67)90031-6
[DNNP] M. Dadarlat, G. Nagy, A. Nemethi, and C. Pasnicu, Reduction of topological stable rank in inductive limits of $C\sp\ast$-algebras, Pacific J. Math. 153 (1992), no. 2, 267–276.
Mathematical Reviews (MathSciNet): MR93d:46119
Zentralblatt MATH: 0809.46054
Project Euclid: euclid.pjm/1102635832
[Eff] E. G. Effros, Dimensions and $C\sp\ast$-algebras, CBMS Regional Conference Series in Mathematics, vol. 46, Conference Board of the Mathematical Sciences, Washington, D.C., 1981.
Mathematical Reviews (MathSciNet): MR84k:46042
Zentralblatt MATH: 0475.46050
[EHS] E. G. Effros, D. Handelman, and C.-L. Shen, Dimension groups and their affine representations, Amer. J. Math. 102 (1980), no. 2, 385–407.
Mathematical Reviews (MathSciNet): MR83g:46061
Zentralblatt MATH: 0457.46047
Digital Object Identifier: doi:10.2307/2374244
[Ell1] G. A. Elliott, On the classification of inductive limits of sequences of semisimple finite-dimensional algebras, J. Algebra 38 (1976), no. 1, 29–44.
Mathematical Reviews (MathSciNet): MR53:1279
Zentralblatt MATH: 0323.46063
Digital Object Identifier: doi:10.1016/0021-8693(76)90242-8
[Ell2] G. A. Elliott, On the classification of $C\sp\ast$-algebras of real rank zero, J. Reine Angew. Math. 443 (1993), 179–219.
Mathematical Reviews (MathSciNet): MR94i:46074
Zentralblatt MATH: 0809.46067
Digital Object Identifier: doi:10.1515/crll.1993.443.179
[EE] G. A. Elliott and D. E. Evans, The structure of the irrational rotation $C\sp\ast$-algebra, Ann. of Math. (2) 138 (1993), no. 3, 477–501.
Mathematical Reviews (MathSciNet): MR94j:46066
Zentralblatt MATH: 0847.46034
Digital Object Identifier: doi:10.2307/2946553
[EG] G. A. Elliott and G. Gong, On inductive limits of matrix algebras over the two-torus, Amer. J. Math. 118 (1996), no. 2, 263–290.
Mathematical Reviews (MathSciNet): MR97g:46073
Zentralblatt MATH: 0847.46032
Digital Object Identifier: doi:10.1353/ajm.1996.0013
[EL] R. Exel and T. Loring, Extending cellular cohomology to $C\sp\ast$-algebras, Trans. Amer. Math. Soc. 329 (1992), no. 1, 141–160.
Mathematical Reviews (MathSciNet): MR92e:46137
Zentralblatt MATH: 0754.46041
Digital Object Identifier: doi:10.2307/2154081
[GL] G. Gong and H. Lin, The exponential rank of inductive limit $C\sp\ast$-algebras, Math. Scand. 71 (1992), no. 2, 301–319.
Mathematical Reviews (MathSciNet): MR94g:46060
Zentralblatt MATH: 0792.46039
[G1] K. R. Goodearl, Notes on a class of simple $C\sp \ast$-algebras with real rank zero, Publ. Mat. 36 (1992), no. 2A, 637–654 (1993).
Mathematical Reviews (MathSciNet): MR94f:46092
Zentralblatt MATH: 0812.46052
[G2] K. R. Goodearl, Partially ordered abelian groups with interpolation, Mathematical Surveys and Monographs, vol. 20, American Mathematical Society, Providence, RI, 1986.
Mathematical Reviews (MathSciNet): MR88f:06013
Zentralblatt MATH: 0589.06008
[Hu] D. Husemoller, Fibre bundles, McGraw-Hill Book Co., New York, 1966.
Mathematical Reviews (MathSciNet): MR37:4821
Zentralblatt MATH: 0144.44804
[Lin1] H. Lin, Ideals of multiplier algebras of simple AF $C\sp \ast$-algebras, Proc. Amer. Math. Soc. 104 (1988), no. 1, 239–244.
Mathematical Reviews (MathSciNet): MR89j:46065
Zentralblatt MATH: 0672.46033
Digital Object Identifier: doi:10.2307/2047494
[Lin2] H. Lin, Generalized Weyl-von Neumann theorems, Internat. J. Math. 2 (1991), no. 6, 725–739.
Mathematical Reviews (MathSciNet): MR92m:46087
Zentralblatt MATH: 0768.46035
Digital Object Identifier: doi:10.1142/S0129167X91000405
[Lin3] H. Lin, The generalized Weyl-von Neumann theorem and $C\sp \ast$-algebra extensions, Algebraic methods in operator theory, Birkhäuser Boston, Boston, MA, 1994, pp. 134–143.
Mathematical Reviews (MathSciNet): MR95h:46084
Zentralblatt MATH: 0824.46062
[Lin4] H. Lin, $C\sp\ast$-algebra extensions of $C(X)$, Mem. Amer. Math. Soc. 115 (1995), no. 550, vi+89.
Mathematical Reviews (MathSciNet): MR96b:46098
Zentralblatt MATH: 0859.46038
[Lin5] H. Lin, Exponential rank of $C\sp\ast$-algebras with real rank zero and the Brown-Pedersen conjectures, J. Funct. Anal. 114 (1993), no. 1, 1–11.
Mathematical Reviews (MathSciNet): MR95a:46079
Zentralblatt MATH: 0812.46054
Digital Object Identifier: doi:10.1006/jfan.1993.1060
[Lin6] H. Lin, Approximation by normal elements with finite spectra in simple AF-algebras, J. Operator Theory 31 (1994), no. 1, 83–98.
Mathematical Reviews (MathSciNet): MR96b:46077
Zentralblatt MATH: 0846.46038
[Lin7] H. Lin, Simple $C\sp\ast$-algebras with continuous scales and simple corona algebras, Proc. Amer. Math. Soc. 112 (1991), no. 3, 871–880.
Mathematical Reviews (MathSciNet): MR92e:46118
Zentralblatt MATH: 0744.46048
Digital Object Identifier: doi:10.2307/2048712
[Lin8] H. Lin, Approximation by normal elements with finite spectra in $C^\ast$-algebras of real rank zero, to appear in Pacific J. Math. 173, 1996.
Mathematical Reviews (MathSciNet): MR1394400
Zentralblatt MATH: 0860.46039
Project Euclid: euclid.pjm/1102365633
[LZ] H. Lin and S. Zhang, On infinite simple $C\sp\ast$-algebras, J. Funct. Anal. 100 (1991), no. 1, 221–231.
Mathematical Reviews (MathSciNet): MR92m:46088
Zentralblatt MATH: 0774.46029
Digital Object Identifier: doi:10.1016/0022-1236(91)90109-I
[Ma] S. Mardesic, On covering dimension and inverse limits of compact spaces, Illinois J. Math. 4 (1960), 278–291.
Mathematical Reviews (MathSciNet): MR22:7101
Zentralblatt MATH: 0094.16902
Project Euclid: euclid.ijm/1255455869
[Ph1] N. C. Phillips, Simple $C\sp \ast$-algebras with the property weak (FU), Math. Scand. 69 (1991), no. 1, 127–151.
Mathematical Reviews (MathSciNet): MR93d:46121
Zentralblatt MATH: 0725.46036
[Ph2] N. C. Phillips, Approximation by unitaries with finite spectrum in purely infinite $C\sp\ast$-algebras, J. Funct. Anal. 120 (1994), no. 1, 98–106.
Mathematical Reviews (MathSciNet): MR95c:46092
Zentralblatt MATH: 0814.46048
Digital Object Identifier: doi:10.1006/jfan.1994.1025
[Pt] I. Putnam, The invertible elements are dense in the irrational rotation $C\sp\ast$-algebras, J. Reine Angew. Math. 410 (1990), 160–166.
Mathematical Reviews (MathSciNet): MR92a:46078
Zentralblatt MATH: 0697.46027
Digital Object Identifier: doi:10.1515/crll.1990.410.160
[Rf] M. Rieffel, $C\sp\ast$-algebras associated with irrational rotations, Pacific J. Math. 93 (1981), no. 2, 415–429.
Mathematical Reviews (MathSciNet): MR83b:46087
Zentralblatt MATH: 0499.46039
Project Euclid: euclid.pjm/1102736269
[Rf2] M. Rieffel, The cancellation theorem for projective modules over irrational rotation $C\sp\ast$-algebras, Proc. London Math. Soc. (3) 47 (1983), no. 2, 285–302.
Mathematical Reviews (MathSciNet): MR85g:46085
Zentralblatt MATH: 0541.46055
Digital Object Identifier: doi:10.1112/plms/s3-47.2.285
[S] S. Sakai, $C\sp*$-algebras and $W\sp*$-algebras, Springer-Verlag, New York, 1971.
Mathematical Reviews (MathSciNet): MR56:1082
Zentralblatt MATH: 0219.46042
[V1] D. Voiculescu, Remarks on the singular extension in the $C\sp\ast$-algebra of the Heisenberg group, J. Operator Theory 5 (1981), no. 2, 147–170.
Mathematical Reviews (MathSciNet): MR82m:46075
Zentralblatt MATH: 0476.22008
[V2] D. Voiculescu, Asymptotically commuting finite rank unitary operators without commuting approximants, Acta Sci. Math. (Szeged) 45 (1983), no. 1-4, 429–431.
Mathematical Reviews (MathSciNet): MR85d:47035
Zentralblatt MATH: 0538.47003
[Wh] G. W. Whitehead, Elements of homotopy theory, Graduate Texts in Mathematics, vol. 61, Springer-Verlag, New York, 1978.
Mathematical Reviews (MathSciNet): MR80b:55001
Zentralblatt MATH: 0406.55001
[Zh1] S. Zhang, $C\sp\ast$-algebras with real rank zero and the internal structure of their corona and multiplier algebras. III, Canad. J. Math. 42 (1990), no. 1, 159–190.
Mathematical Reviews (MathSciNet): MR94i:46095
Zentralblatt MATH: 0770.46026
[Zh2] S. Zhang, Certain $C\sp \ast$-algebras with real rank zero and their corona and multiplier algebras. I, Pacific J. Math. 155 (1992), no. 1, 169–197.
Mathematical Reviews (MathSciNet): MR94i:46093
Zentralblatt MATH: 0816.46057
Project Euclid: euclid.pjm/1102635475
[Zh3] S. Zhang, Certain $C\sp \ast$-algebras with real rank zero and their corona and multiplier algebras. II, $K$-Theory 6 (1992), no. 1, 1–27.
Mathematical Reviews (MathSciNet): MR94i:46094
Zentralblatt MATH: 0816.46058
Digital Object Identifier: doi:10.1007/BF00961332
[Zh4] S. Zhang, $C\sp\ast$-algebras with real rank zero and their corona and multiplier algebras. IV, Internat. J. Math. 3 (1992), no. 2, 309–330.
Mathematical Reviews (MathSciNet): MR94i:46096
Zentralblatt MATH: 0772.46032
Digital Object Identifier: doi:10.1142/S0129167X92000102
[Zh5] S. Zhang, A Riesz decomposition property and ideal structure of multiplier algebras, J. Operator Theory 24 (1990), no. 2, 209–225.
Mathematical Reviews (MathSciNet): MR93b:46116
Zentralblatt MATH: 0747.46043
[Zh6] S. Zhang, On the structure of projections and ideals of corona algebras, Canad. J. Math. 41 (1989), no. 4, 721–742.
Mathematical Reviews (MathSciNet): MR90h:46094
Zentralblatt MATH: 0668.46031
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