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)

 
 

 

Splitting for subalgebras of tensor products


Author: Joachim Zacharias
Journal: Proc. Amer. Math. Soc. 129 (2001), 407-413
MSC (2000): Primary 46L06, 46L45
DOI: https://doi.org/10.1090/S0002-9939-00-05629-X
Published electronically: July 27, 2000
MathSciNet review: 1706957
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract:

We prove splitting results for subalgebras of tensor products of operator algebras. In particular, any $C^*$-algebra $C$ s.t. $A\otimes 1 \subseteq C \subseteq A \otimes B$ is a tensor product $A\otimes B_0 $ provided $A$ is simple and nuclear.


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

  • [An79] J. Anderson: Extensions, restrictions, and representations of states on $C^*$-algebras, Trans. AMS 249 No.2 (1979), 303-329 MR 80k:46069
  • [Bl96] E. Blanchard: Déformations de $C^*$-algèbres de Hopf, Bull. Soc. Math. France 124 (1996), 141-215 MR 97f:46092
  • [Bl95] E. Blanchard: Tensor products of $C(X)$-algebras over $C(X)$, Astérisque 232 (1995), 81-92 MR 96m:46100
  • [Cu77] J. Cuntz: The structure of multiplication and addition in simple $C^*$-algebras, Math. Scand. 40 (1977), 215-233 MR 58:17862
  • [DH85] J. DeCanniere, U. Haagerup: Multipliers of the Fourier algebra of some simple groups and their discrete subgroups, Amer. J. Math. 107 (1985) 455-500 MR 86m:43002
  • [GK96] L. Ge, R. Kadison: On tensor products of von Neumann algebras, Invent. Math. 123 (1996), 453-466 MR 97c:46074
  • [Ki94a] E. Kirchberg: Exact $C^*$-algebras, tensor products and the classification of purely infinite $C^*$-algebras, Proc. ICM 1994, 943-954 MR 97g:46074
  • [Ki94b] E. Kirchberg: Classification of purely infinite $C^*$-algebras using Kasparov's theory, preprint (1994)
  • [KW95] E. Kirchberg, S. Wassermann: Operations on continuous bundles of $C^*$-algebras, Math. Ann. 303 (1995), 677-697 MR 96j:46057
  • [Na72] M. A. Naimark: Normed rings, Groningen 1972
  • [SZ98] S. Stratila, L. Zsido: A commutation theorem in tensor products of von Neumann algebras, preprint (1998) CMP 99:15
  • [Wa76] S. Wassermann: The slice map problem for $C^*$-algebras, Proc. London Math. Soc. 36, (1976), 537-559 MR 53:14152
  • [Wa78] S. Wassermann: A pathology in the ideal space of $L(H) \otimes L(H)$, Indiana Univ. Math. J. 27 (1978), 1012-1020 MR 80d:46113
  • [Zs98] L. Zsido: A criterion for splitting $C^*$-algebras in tensor products, to appear in Proc. AMS CMP 99:04

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 46L06, 46L45

Retrieve articles in all journals with MSC (2000): 46L06, 46L45


Additional Information

Joachim Zacharias
Affiliation: Département de Mathématiques, UFR Université d’Orléans, Rue de Chartres - BP 6759, 45067 Orléans Cedex 2, France
Address at time of publication: School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD England
Email: zacharia@labomath.univ-orleans.fr

DOI: https://doi.org/10.1090/S0002-9939-00-05629-X
Keywords: Tensor products, splitting, slice map property
Received by editor(s): April 9, 1999
Published electronically: July 27, 2000
Additional Notes: This research was supported by the European Community.
Communicated by: David R. Larson
Article copyright: © Copyright 2000 American Mathematical Society

American Mathematical Society