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)

 
 

 

Locally pre-$C$*-equivalent algebras


Author: Wei Wu
Journal: Proc. Amer. Math. Soc. 131 (2003), 555-562
MSC (2000): Primary 46K10
DOI: https://doi.org/10.1090/S0002-9939-02-06686-8
Published electronically: June 3, 2002
MathSciNet review: 1933347
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We prove a weaker form of Cuntz's theorem: every locally pre-$C^*$-equivalent Banach *-algebra is $C^*$-equivalent. Using this result, we obtain local conditions for the existence of an equivalent $C^*$-norm.


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

  • 1. E. M. Alfsen and F. W. Shultz, On orientation and dynamics in operator algebras, Commun. Math. Phys., 194 (1998), 87-108. MR 99h:46129
  • 2. B. A. Barnes, Locally $B^*$-equivalent algebras, Trans. Amer. Math. Soc., 167 (1972), 435-442. MR 45:5763
  • 3. B. A. Barnes, Locally $B^*$-equivalent algebras, II, Trans. Amer. Math. Soc., 176 (1973), 297-303. MR 47:9296
  • 4. F. F. Bonsall and J. Duncan, Complete normed algebras, Springer-Verlag, Berlin-Heidelberg-New York, 1973. MR 54:11013
  • 5. J. Cuntz, Locally $C^*$-equivalent algebras, J. Funct. Anal., 32 (1976), 95-106. MR 56:6398
  • 6. R. S. Doran and V. A. Belfi, Characterizations of $C^*$-algebras, the Gelfand-Naimark theorems, Marcel Dekler, Inc., New York and Basel, 1986. MR 87k:46115
  • 7. T. W. Hungerford, Algebras, Graduate Texts in Mathematics 73, Springer-Verlag, Berlin-Heidelberg-New York, 1974. MR 82a:00006
  • 8. I. Kaplansky, Normed algebras, Duke Math. J., 16 (1949), 399-418. MR 11:115
  • 9. B.-R. Li, Introduction to operator algebras, World Scientific, Singapore, 1992. MR 94b:46083
  • 10. Z. Magyar, A characterization of (real or complex) Hermitian algebras and equivalent $C^*$-algebras, Acta Sci. Math. (Szeged), 53 (1989), 345-353. MR 91c:46077
  • 11. Z. Magyar, Conditions for hermiticity and for existence of an equivalent $C^*$-norm, Acta Sci. Math. (Szeged), 46 (1983), 305-310. MR 86b:46085
  • 12. Z. Magyar, A sharpening of the Berkson-Glickfeld theorem, Proc. Edinburgh Math. Soc., 26 (1983), 275-278. MR 85c:46057
  • 13. V. Pták, Banach algebras with involution, Manuscripta Math., 6 (1972), 245-290. MR 45:5764
  • 14. M. A. Rieffel, Metrics on state spaces, Doc. Math., 4 (1999), 559-600. MR 2001g:46154
  • 15. S. Sakai, $C^*$-algebras and $W^*$-algebras, Springer-Verlag, Berlin-Heidelberg-New York, 1971. MR 56:1082
  • 16. I. E. Segal, Postulates for general quantum mechanics, Ann. of Math., 48 (1947), 930-948. MR 9:241
  • 17. B. Yood, Faithful *-representations of normed algebras, Pacific J. Math., 10 (1960), 345-363. MR 22:1826
  • 18. B. Yood, On axioms for B*-algebras, Bull. Amer. Math. Soc., 76 (1970), 80-82. MR 40:6273

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 46K10

Retrieve articles in all journals with MSC (2000): 46K10


Additional Information

Wei Wu
Affiliation: Department of Mathematics, East China Normal University, Shanghai 200062, People’s Republic of China
Email: wwu@math.ecnu.edu.cn

DOI: https://doi.org/10.1090/S0002-9939-02-06686-8
Keywords: $C^*$-equivalent algebra, pre-$C^*$-equivalent, locally pre-$C^*$-equivalent
Received by editor(s): September 27, 2001
Published electronically: June 3, 2002
Additional Notes: The author was supported in part by Shanghai Priority Academic Discipline
Communicated by: David R. Larson
Article copyright: © Copyright 2002 American Mathematical Society

American Mathematical Society