Geodesic
Homomorphisms From C(X) Into C*-Algebras
Canadian journal of mathematics, Tome 49 (1997) no. 5, pp. 963-1009

Voir la notice de l'article provenant de la source Cambridge University Press

Let A be a simple C *-algebra with real rank zero, stable rank one and weakly unperforated K 0(A) of countable rank. We show that a monomorphism Φ: C(S 2) → A can be approximated pointwise by homomorphisms from C(S 2) into A with finite dimensional range if and only if certain index vanishes. In particular,we show that every homomorphism φ from C(S 2) into a UHF-algebra can be approximated pointwise by homomorphisms from C(S 2) into the UHF-algebra with finite dimensional range.As an application, we show that if A is a simple C*-algebra of real rank zero and is an inductive limit of matrices over C(S 2) then A is an AF-algebra. Similar results for tori are also obtained. Classification of Hom (C(X), A) for lower dimensional spaces is also studied.
DOI : 10.4153/CJM-1997-050-9
Mots-clés : 46L05, 46L80, 46L35, Homomorphism of C(S 2), approximation, real rank zero, classification 
Lin, Huaxin. Homomorphisms From C(X) Into C*-Algebras. Canadian journal of mathematics, Tome 49 (1997) no. 5, pp. 963-1009. doi: 10.4153/CJM-1997-050-9
@article{10_4153_CJM_1997_050_9,
     author = {Lin, Huaxin},
     title = {Homomorphisms {From} {C(X)} {Into} {C*-Algebras}},
     journal = {Canadian journal of mathematics},
     pages = {963--1009},
     year = {1997},
     volume = {49},
     number = {5},
     doi = {10.4153/CJM-1997-050-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1997-050-9/}
}
TY  - JOUR
AU  - Lin, Huaxin
TI  - Homomorphisms From C(X) Into C*-Algebras
JO  - Canadian journal of mathematics
PY  - 1997
SP  - 963
EP  - 1009
VL  - 49
IS  - 5
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1997-050-9/
DO  - 10.4153/CJM-1997-050-9
ID  - 10_4153_CJM_1997_050_9
ER  - 
%0 Journal Article
%A Lin, Huaxin
%T Homomorphisms From C(X) Into C*-Algebras
%J Canadian journal of mathematics
%D 1997
%P 963-1009
%V 49
%N 5
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1997-050-9/
%R 10.4153/CJM-1997-050-9
%F 10_4153_CJM_1997_050_9

Exel, R. and Loring, T.A., Almost commuting unitary matrices. Proc. Amer. Math. Soc. 106(1989), 913–915. Google Scholar

Exel, R. and Loring, T.A., Invariants of almost commuting unitaries. J. Funct. Anal. 95(1991), 364–376. Google Scholar

Exel, R. and Loring, T.A., An Extension of cellular cohomology to C*-algebras. Trans. Amer. Math. Soc. 392(1992), 141–160. Google Scholar

Gong, G. and Lin, H., Exponential rank of inductive limit C*-algebras. Math. Scand. 71(1992), 301–319. Google Scholar

Goodearl, K.R.,Notes on a class of simpleC*-algebras with real rank zero. Publ.Mat. 36(1992), 637–654. Google Scholar

Halmos, P.R., Some unsolved problems of unknown depth about operators on Hilbert space. Proc. Roy. Soc. Edinburgh Sect. A 76(1976), 67–76. Google Scholar

Jensen, H.E., Scattered C*-algebras. Math. Scand. 41(1977), 308–314. Google Scholar

Lin, H., Ideals of multiplier algebras of simple AF C*-algebras. Proc. Amer. Math. Soc. 104(1988), 239–244. Google Scholar

Lin, H., The structure of quasimultipliers of C*-algebras. Trans. Amer.Math. Soc. 315(1989), 147–172. Google Scholar

Lin, H., Simple C*-algebras with continuous scales and simple corona algebras. Proc. Amer. Math. Soc. 112(1991), 871–880. Google Scholar

Lin, H., Skeleton C*-subalgebras. Canad. J. Math. 44(1992), 324–343. Google Scholar

Lin, H., Generalized Weyl-von Neumann theorems. Internat. J. Math. 2(1991), 725–739. Google Scholar

Lin, H., Generalized Weyl-von Neumann theorems II. Math. Scand. 77(1995), 129–147. Google Scholar

Lin, H., C*-algebra extensions of C (X). Mem. Amer. Math. Soc. (550) 115(1995). Google Scholar

Lin, H., Exponential rank of C*-algebras with real rank zero and Brown-Pedersen's conjectures. J. Funct. Anal. 114(1993), 1–11. Google Scholar

Lin, H., Approximation by normal elementswith finite spectra in simple AF-algebras. J.Operator Theory 31(1994), 83–98. Google Scholar

Lin, H., Approximation by normal elements with finite spectra in C*-algebras of real rank zero. Pacific J. Math. 173(1996), 443–489. Google Scholar

Lin, H., The generalized Berg theorem and BDF-theorem. Trans. Amer.Math. Soc. 349(1997). 529–545. Google Scholar

Lin, H., Extensions by C*-algebras of real rank zero II. Proc. London Math. Soc. 71(1995), 641–674. Google Scholar

Lin, H., and Rørdam, M., Extensions of inductive limits of circle algebras. J. LondonMath. Soc. 51(1995), 603–613. Google Scholar

Lin, H. and Zhang, S., Infinite simple C*-algebras. J. Funct.Anal. 100(1991), 221–231. Google Scholar

Loring, T.A., K-theory and asymptotically commuting matrices. Canad. J. Math. 40(1988), 197–216. Google Scholar

Loring, T.A., The noncommutative topology of one-dimensional spaces. Pacific J. Math. 136(1989). 145–158. Google Scholar

Mingo, J., K-theory and multipliers of stable C*-algebras. Trans. Amer.Math. Soc. 299(1987), 397–412. Google Scholar

Newman, M.H.A., Topology of the Plane Sets. Cambridge University Press (1951). Google Scholar

Pearcy, C. and Shields, A., Almost commuting matrices. J. Funct. Anal. 33(1979), 332–338. Google Scholar

Pedersen, G.K., C*-Algebras and their Automorphism Groups. Academic Press, New York, 1979. Google Scholar

Phillips, N.C., Simple C*-algebras with property weak (FU). Math. Scand. 69(1991), 127–151. Google Scholar

Phillips, N.C., Approximation by unitaries with finite spectrum in purely infinite simple C*-algebras. J. Funct. Anal. 120(1994), 98–106. Google Scholar

Phillips, N.C., Reduction of exponential rank in direct limits of C*-algebras. Canad. J. Math. 46(1994). 818–853. Google Scholar

Putman, I., The invertible elements are dense in the irrational rotation C*-algebras. J. Reine Angew.Math. 410(1990), 160–166. Google Scholar

Rieffel, M., C*-algebras associated with irrational rotations. Pacific J. Math. 93(1981), 415–429. Google Scholar

Rieffel, M., Dimensions and stable rank in the K-theory of C*-algebras. Proc. LondonMath. Soc. 46(1983), 301–333. Google Scholar

Rieffel, M. Asymptotically commuting finite rank unitaries without commuting approximants. Acta Sci.Math. 451(1983), 429–431. Google Scholar

Zhang, S., 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. Google Scholar

Zhang, S., Certain C*-algebras with real rank zero and their corona andmultiplier algebras, Part I. Pacific J. Math. 155(1992), 169–197. Google Scholar

Zhang, S., Certain C*-algebras with real rank zero and their corona and multiplier algebras, Part II. K-theory 6(1992), 1–27. Google Scholar

Zhang, S., Certain C*-algebras with real rank zero and their corona and multiplier algebras, Part IV. Internat. J. Math. 3(1992), 309–330. Google Scholar

Zhang, S., A Riesz decomposition property and ideal structure of multiplier algebras. J. Operator Theory 24(1990), 209–225. Google Scholar

Zhang, S., On the structure of projections and ideals of corona algebras. Canad. J. Math. 61(1989). 721–742. Google Scholar

Zhang, S., The cancellation theorem for projective modules over irrational rotation algebras. Proc. London Math. Soc. 47(1983), 258–302. Google Scholar

Schaffer, J.J., On unitary dilations of contractions. Proc. Amer. Math. Soc. 6(1955), 322. Google Scholar

Su, H., 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). Google Scholar

Voiculescu, D., Remarks on the singular extension in the C*-algebra of the Heisenberg group. J.Operator Theory 5(1981), 147–170. Google Scholar

Cité par Sources :