Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Semiprojectivity of universal $ C^*$-algebras generated by algebraic elements


Author: Tatiana Shulman
Journal: Proc. Amer. Math. Soc. 140 (2012), 1363-1370
MSC (2010): Primary 46L05, 46L35
DOI: https://doi.org/10.1090/S0002-9939-2011-11144-4
Published electronically: August 9, 2011
MathSciNet review: 2869120
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ p$ be a polynomial in one variable whose roots all have multiplicity more than 1. It is shown that the universal $ C^*$-algebra of a relation $ p(x)=0$, $ \Vert x\Vert \le 1$, is semiprojective and residually finite-dimensional. Applications to polynomially compact operators are given.


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

  • 1. C. A. Akemann and G. K. Pedersen, Ideal perturbations of elements in $ C^*$-algebras, Math. Scand. 41 (1977), 117-139. MR 0473848 (57:13507)
  • 2. B. Blackadar, Shape theory for $ C^*$-algebras, Math. Scand. 56 (1985), 249 - 275. MR 813640 (87b:46074)
  • 3. C. K. Chui, D. A. Legg, P. W. Smith, and J. D. Ward, On a question of Olsen concerning compact perturbations of operators, Michigan Math. J. 24, 1 (1977), 119-127. MR 0451005 (56:9295)
  • 4. D. Hadwin, Lifting algebraic elements in $ C^*$-algebras, J. Funct. Anal. 127 (1995), 431-437. MR 1317724 (95m:46092)
  • 5. T. A. Loring, Lifting solutions to perturbing problems in $ C^*$-algebras, volume 8 of Fields Institute Monographs. American Mathematical Society, Providence, RI, 1997. MR 1420863 (98a:46090)
  • 6. T. A. Loring, G. K. Pedersen, Smoothing techniques in $ C^*$-algebra theory, J. Operator Theory 37 (1997), 3-21. MR 1438197 (98c:46122)
  • 7. G. J. Murphy, $ C^*$-algebras and operator theory, Academic Press, Boston-New York, 1990. MR 1074574 (91m:46084)
  • 8. C. L. Olsen and G. K. Pedersen, Corona $ C^*$-algebras and their applications to lifting problems, Math. Scand. 64 (1989), 63-86. MR 1036429 (91g:46064)
  • 9. C. L. Olsen, A structure theorem for polynomially compact operators, Amer. J. Math. 93 (1971), 686-698. MR 0405152 (53:8947)
  • 10. C. L. Olsen and J. K. Plastiras, Quasialgebraic operators, compact perturbations, and the essential norm, Michigan Math. J. 21 (1974), 385-397 (1975). MR 0365205 (51:1458)
  • 11. C. L. Olsen, Norms of compact perturbations of operators, Pacific J. Math. 68, 1 (1977), 209-228. MR 0451010 (56:9300)
  • 12. G. K. Pedersen, $ C^*$-algebras and Their Automorphism Groups, LMS Monographs 14, Academic Press, London-New York, 1979. MR 548006 (81e:46037)
  • 13. T. Shulman, Lifting of nilpotent contractions, Bull. London Math. Soc. 40, 6 (2008), 1002-1006. MR 2471949 (2009k:46102)
  • 14. R. R. Smith and J. D. Ward, A note on polynomial operator approximation, Proc. Amer. Math. Soc. 88, 3 (1983), 491-494. MR 699420 (84j:47008)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 46L05, 46L35

Retrieve articles in all journals with MSC (2010): 46L05, 46L35


Additional Information

Tatiana Shulman
Affiliation: Department of Mathematical Sciences, University of Copenhagen, Universitet- sparken 5, DK-2100 Copenhagen, Denmark
Email: shulman@math.ku.dk, tatiana_shulman@yahoo.com

DOI: https://doi.org/10.1090/S0002-9939-2011-11144-4
Keywords: Projective and semiprojective $C^{*}$-algebras, stable relation, lifting problem, $M$-ideal
Received by editor(s): June 13, 2009
Received by editor(s) in revised form: January 5, 2011
Published electronically: August 9, 2011
Communicated by: Marius Junge
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

American Mathematical Society