Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Extensions contained in ideals


Author: Dan Kucerovsky
Journal: Trans. Amer. Math. Soc. 356 (2004), 1025-1043
MSC (2000): Primary 19K35; Secondary 46L85, 46L80
DOI: https://doi.org/10.1090/S0002-9947-03-03297-5
Published electronically: August 25, 2003
MathSciNet review: 1984466
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We prove a Weyl-von Neumann type absorption theorem for extensions which are not full, and give a condition for constructing infinite repeats contained in an ideal. We also clear up some questions associated with the purely large criterion for full extensions to be absorbing.


References [Enhancements On Off] (What's this?)

  • 1. C.A. Akemann, J. Anderson, and G.K. Pedersen. Excising states of $C^{*}$-algebras, Canad. J. Math. 38 (1986). MR 88d:46107
  • 2. L. Brown. Stable isomorphism of hereditary subalgebras of $C^{*}$-algebras, Pacific J. Math 71 (1977), 335-384. MR 56:12894
  • 3. L. Brown, R. Douglas, P. Fillmore, Unitary equivalence modulo the compact operators and extensions of $C^{*}$-algebras, Lecture Notes in Math. 345 (1973), 58-128. MR 52:1378
  • 4. P.J. Cohen, Factorization in Group Algebras, Duke Math. J. 26 (1959), 199-205. MR 21:3729
  • 5. G.A. Elliott, Derivations of matroid $C^{*}$-algebras, II, Ann. of Math 100 (1974), 407-422. MR 50:5485
  • 6. G.A. Elliott, D. Kucerovsky, An abstract Brown-Douglas-Fillmore absorption theorem, Pacific J. of Math. 198 (2001), 385-409. MR 2002i:46052
  • 7. G.G. Kasparov, Hilbert $C^{*}$-modules: theorems of Stinespring and Voiculescu, J. Op. Th. 4 (1980), 133-150. MR 82b:46074
  • 8. E. Kirchberg, The classification of purely infinite $C^{*}$-algebras using Kasparov's theory $K$-theory, preprint, 1995.
  • 9. E. Kirchberg and M. Rørdam, Nonsimple purely infinite $C^{*}$-algebras, preprint, 1999. MR 2001k:46088
  • 10. J. Hjelmborg and M. Rørdam, Stablility of $C^{*}$-algebras, JFA, 1998. MR 99g:46079
  • 11. J.A. Mingo, K-theory and multipliers of stable $C^{*}$-algebras, Tr. AMS. 299 (1987), 397-411. MR 88f:46136
  • 12. G.K. Pedersen, A strict version of the non-commutative Urysohn lemma, Proc. AMS. 125 (1997), 2657-2660. MR 97j:46061
  • 13. M. Rørdam, Ideals in the multiplier algebra of a stable $C^{*}$-algebra, J. Op. Th. 25 (1991), 283-298. MR 94c:46118
  • 14. S. Zhang, Certain $C^{*}$-algebras with real rank zero and their corona and multiplier algebras, Part I, Pacific J. Math. 155 (1992), 169-197. MR 94i:46093

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 19K35, 46L85, 46L80

Retrieve articles in all journals with MSC (2000): 19K35, 46L85, 46L80


Additional Information

Dan Kucerovsky
Affiliation: Department of Mathematics and Statistics, University of New Brunswick-Fredericton, Fredericton, New Brunswick, Canada E3B 5A3
Email: dkucerov@unb.ca

DOI: https://doi.org/10.1090/S0002-9947-03-03297-5
Keywords: KK--theory, classification of operator algebras, absorbing extensions
Received by editor(s): July 29, 2002
Published electronically: August 25, 2003
Additional Notes: This research was supported by the NSERC, under grant # 228065–00
Article copyright: © Copyright 2003 American Mathematical Society

American Mathematical Society