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Skeleton C*-Subalgebras

Published online by Cambridge University Press:  20 November 2018

Huaxin Lin
Huaxin Lin*
Affiliation:
Department of Mathematics East China Normal University Shanghai 200062, China
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Abstract

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We study skeleton C*-subalgebras of a given C*-algebra. We show that if A is a unital (non-unital but σ-unital) simple C*-algebra, ℳ is any unital (nonunital) matroid C* -algebra, then A contains a skeleton C*-subalgebra B with a quotient which is isomorphic to ℳ. Other results for skeleton C*-subalgebras are also obtained. Applications of these results to the structure of quasi-multipliers and perturbations of C*-algebras are given.

Keywords

Primary:46L05
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 44 , Issue 2 , 01 April 1992 , pp. 324 - 341
Copyright
Copyright © Canadian Mathematical Society 1992

References

1. Akemann, C.A. and Pedersen, G.K., Complications of semi-continuity in C*-algebra theory, Duke Math. J. 40(1973), 785–795.Google Scholar
2. Blackadar, B., K-Theory for Operator Algebras. Mathematical Sciences Research Institute Publications, Springer-Verlag, New York, Berlin, Heidelberg, 1986.Google Scholar
3. Blackadar, B. and Handelman, D., Dimension functions and traces on C*-algebras, J. Functional Anal. 45(1982), 297–340.Google Scholar
4. Brown, L.G., Close hereditary C*-subalgebras and the structure of quasi-multipliers, to appear.Google Scholar
5. Brown, L.G. and Pedersen, G.K., C* -algebras of real rank zero, preprint.Google Scholar
6. Choi, M.-D. and Christensen, E., Completely order isomorphic and close C*-algebras need not be *-isomorphic, Bull. London Math. Soc. 57(1983), 604–610.Google Scholar
7. Choi, M.-D. and Elliott, G.A., Density of the self-adjoint elements with finite spectrum in an irrational rotation C* -algebra, preprint.Google Scholar
8. Christensen, E., Perturbations of operator algebras, Invent. Math. J. 43(1977), 1–13.Google Scholar
9. Christensen, E., Near inclusions of C*-algebras, Acta Math. 144(1980), 249–265.Google Scholar
10. Cuntz, J., The structure of addition and multiplication in simple C*-algebras, Math. Scand. 40(1977), 215- 233.Google Scholar
11. Cuntz, J., Dimension functions on simple C*-algebras, Math. Ann. 233(1978), 145–153.Google Scholar
12. Cuntz, J., The internal structure of simple C*-algebras, in “Operator Algebras and Applications” , ed. Kadison, R.V., Proc. Symp. Pure Math. 38, Part 1, Amer. Math. Soc, Providence, 1981. 85–115.Google Scholar
13. Cuntz, J. and Pedersen, G.K., Equivalence and traces on C*-algebras, J. Functional Anal. 33(1979), 135- 164.Google Scholar
14. Dixmier, J., On some C*-algebras considered by Glimm, J. Functional Anal. 1(1967), 182–203.Google Scholar
15. Effros, E., Dimensions and C* -algebras. CBMS Regional Conf. Ser. in Math., 46 Amer. Math. Soc, Providence, 1981.Google Scholar
16. Jensen, H.E., Scattered C*-algebras, Math. Scand. 41(1977), 308–314.Google Scholar
17. Johnson, B.E., Perturbations of Banach algebras, Proc. London Math. Soc. 34(1977), 439–458.Google Scholar
18. Johnson, B.E., A counterexample in the perturbation theory of C*-algebras, Canad. Math. Bull. 25(1982), 311- 316.Google Scholar
19. Lin, H., The structure of quasi-multipliers of C*-algebras, Trans. Amer. Math. Soc. 315(1989), 147–172.Google Scholar
20. Lin, H., Fundamental approximate identities and quasi-multipliers of simple AF C* -algebras, J. Functional Anal. 79(1988), 32–43.Google Scholar
21. Lin, H., The multipliers and quasi-multipliers of simple C*-algebras, preprint.Google Scholar
22. Pedersen, G.K., C* -Algebras and their automorphism groups. Academic Press, New York, London, 1979.Google Scholar
23. Rieffel, M., The cancellation theoremforprojective modules over irrational rotation algebras, Proc. London Math. Soc. 47(1983), 285–302.Google Scholar
24. Zhang, S., Riesz decomposition property and ideal structure of multiplier algebras, J. Operator Theory, to appear.Google Scholar
25. Zhang, S., Certain C*-algebras with real rank zero and their corona and multiplier algebras III, Canad. J. Math., to appear.Google Scholar
26. Zhang, S., Trivial K1 -flow of AF-algebras and finite von Neumann algebras, preprint.Google Scholar