## Pacific Journal of Mathematics

### Reduction of topological stable rank in inductive limits of $C^*$-algebras.

#### Article information

Source
Pacific J. Math., Volume 153, Number 2 (1992), 267-276.

Dates
First available in Project Euclid: 8 December 2004

https://projecteuclid.org/euclid.pjm/1102635832

Mathematical Reviews number (MathSciNet)
MR1151561

Zentralblatt MATH identifier
0809.46054

#### Citation

Dădărlat, Marius; Nagy, Gabriel; Némethi, András; Pasnicu, Cornel. Reduction of topological stable rank in inductive limits of $C^*$-algebras. Pacific J. Math. 153 (1992), no. 2, 267--276. https://projecteuclid.org/euclid.pjm/1102635832

#### References

• [I] B. Blackadar, Symmetries of the CAR algebra,preprint, 1988.
• [2] B. Blackadar, O. Brattelli, G. A. Elliott and A. Kumjian, Reduction of real rank and inductive limits of C*-algebras, preprint.
• [3] B. Blackadar and A. Kumjian, Skew products of relations and the structure of simple C*-algebras, Mat. Z., 189 (1985), 55-63.
• [4] O. Brattelli, Inductive limits of finite-dimensional C*-algebras, Trans. Amer. Math. Soc, 171 (1972), 195-234.
• [5] O. Brattelli, G. A. Elliott, D. E. Evans and A. Kishimoto, Finite group actions on AF algebrasobtained by folding the interval, preprint, 1989.
• [6] L. B. Brown and G. K. Pedersen, C*-algebras of real rank zero, preprint, 1989.
• [7] J. Bunce and J. Deddens, A family of simple C*-algebrasrelated to weighted shift operators, J. Funct. Anal., 19 (1975), 12-34.
• [8] M.-D. Choi and G. A. Elliott, Density of the self adjoint elements with finite spectrum in an irrational rotation C*-algebra, preprint, 1988.
• [9] M. Dadarlat, On homomorphisms of certain C*-algebras, preprint, 1986.
• [10] M. Dadarlat and A. Nemethi,Shape theory and connective K-theory,to appear in J. Operator Theory.
• [II] G. A. Elliott, On the classificationof C*-algebras of real rank zero, preprint.
• [12] D. E. Evans and A. Kishimoto, Compact group actions on UHF algebrasob- tained by folding the interval, J. Funct. Anal, (to appear).
• [13] S. Helgason, Differential Geometry, Lie Groups and Symmetric Spaces, Aca- demic Press, 1978.
• [14] D. Husemoller, Fibre Bundles, 2nd ed., Springer Verlag, 1966.
• [15] A. Kumjian, An involutive automorphism of the Bunce-Deddens algebra, C.R. Math. Rep. Acad. Sci. Canada, 10 (1988), 217-218.
• [16] E. Michael, Continuous selections II,Ann of Math., 64, no. 3, (1956), 562-580.
• [17] G. Nagy, Some remarks on lifting invertibleelementsfrom quotient C*-algebras, J. Operator Theory, 21 (1989), 379-386.
• [18] V. Nistor, Stable rangefor tensor products of extensions of 3? by C(X), J. Operator Theory, 16 (1986), 387-396.
• [19] C. Pasnicu, On inductive limits of certain C*-algebras of the form C(X) <8> F, Trans. Amer. Math. Soc, 310 (1988), 703-714.
• [20] G. K. Pedersen, C*-algebras and their Automorphism Groups, Academic Press, London/New York, 1979.
• [21] I. F. Putnam, Theinvertible elements are dense in the irrational rotation C*- algebras,preprint, 1989.
• [22] N.Riedel, On the topological stable rank of irrational rotation algebras, J. Op- erator Theory, 13 (1985), 143-150.
• [23] M.A. Rieffel, Dimension andstable rank in the K-theory of C*-algebras, Proc. London Math. Soc, 46 (1983), 301-333.
• [24] M.Rordam, Onthe structureofsimple C*-algebras tensoredwith a \JH-algebra I, II,preprints.
• [25] S. Zhang, C*-algebraswith real rank zero and the internal structure of their corona andmultiplier algebras I,II,III,IV, preprints.