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)

 
 

 

Hilbert C$^*-$modules in which all closed submodules are complemented


Author: Bojan Magajna
Journal: Proc. Amer. Math. Soc. 125 (1997), 849-852
MSC (1991): Primary 46L05; Secondary 46C50
DOI: https://doi.org/10.1090/S0002-9939-97-03551-X
MathSciNet review: 1346981
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let $B$ be a C$^*-$algebra. If there exists a full Hilbert $B-$module $X$ such that $X=Y\oplus Y^{\perp }$ for each closed submodule $Y$, then $B$ is *-isomorphic to a C$^*-$algebra of (not neccesarily all) compact operators on a Hilbert space.


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

  • 1. W. B. Arveson, An invitation to C$^*-$algebras, GTM 39, Springer-Verlag, Berlin, 1976. MR 58:23621
  • 2. B. A. Barnes, G. J. Murphy, M. R. F. Smyth and T. T. West, Riesz and Fredholm theory in Banach algebras, Pitman Research Notes in Math. 67, Pitman, 1982. MR 84a:46108
  • 3. L. G. Brown, P. Green and M. A. Rieffel, Stable isomorphism and strong Morita equivalence of C$^*-$algebras, Pacific J. Math. 71 (1977), 349-363. MR 57:3866
  • 4. K. Jensen and K. Thomsen, Elements of KK-theory, Birkh\"auser, Basel, 1991. MR 94b:19008
  • 5. E. C. Lance, Hilbert C$^*-$modules, London Math. Soc Lecture Note Series 210, Cambridge Univ. Press, Cambridge, 1995. CMP 95:10
  • 6. H. Lin, Injective Hilbert C$^*-$modules, Pacific J. Math. 154 (1992), 131-164. MR 93c:46110
  • 7. J. Lindenstrauss and L. Tzafriri, On complemented subspaces problem, Israel J. Math. 9 (1971), 263-269. MR 43:2474
  • 8. G. J. Murphy, C$^*-$algebras and operator theory, Academic Press, London, 1990. MR 91m:46084
  • 9. W. Paschke, Inner product modules over B$^*$-algebras, Trans. Amer. Math. Soc. 182 (1973), 443-468. MR 50:8087
  • 10. M. Rieffel, Induced representations of C$^*-$algebras, Advances in Math. 13 (1974), 176-257. MR 50:5489

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 46L05, 46C50

Retrieve articles in all journals with MSC (1991): 46L05, 46C50


Additional Information

Bojan Magajna
Email: Bojan.Magajna@uni-lj.si

DOI: https://doi.org/10.1090/S0002-9939-97-03551-X
Keywords: Hilbert C$^*-$modules, complemented submodules
Received by editor(s): July 3, 1995
Received by editor(s) in revised form: September 26, 1995
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1997 American Mathematical Society

American Mathematical Society