Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The splitting problem for subspaces of tensor products of operator algebras


Author: Jon Kraus
Journal: Proc. Amer. Math. Soc. 132 (2004), 1125-1131
MSC (2000): Primary 46L10
Published electronically: November 4, 2003
MathSciNet review: 2045429
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The main result of this paper is that if $N$ is a von Neumann algebra that is a factor and has the weak* operator approximation property (the weak* OAP), and if $R$ is a von Neumann algebra, then every $\sigma $-weakly closed subspace of ${{N}\bar \otimes {R}}$that is an ${N}\bar \otimes {\mathbb{C} 1_{R}}$-bimodule (under multiplication) splits, in the sense that there is a $\sigma $-weakly closed subspace $T$ of $R$ such that $S={{N}\bar \otimes {T}}$. Note that if $S$ is a von Neumann subalgebra of ${{N}\bar \otimes {R}}$, then $S$is an ${N}\bar \otimes {\mathbb{C} 1_{R}} $-bimodule if and only if ${N}\bar \otimes {\mathbb{C} 1_{R}} \subset S$. So this result is a generalization (in the case where $N$ has the weak* OAP) of the result of Ge and Kadison that if $N$ is a factor, then every von Neumann subalgebra $M$ of ${{N}\bar \otimes {R}} $ that contains ${N}\bar \otimes {\mathbb{C} 1_{R}}$splits. We also obtain other results concerning the splitting of $\sigma $-weakly closed subspaces of tensor products of von Neumann algebras and the splitting of normed closed subspaces of C*-algebras that generalize results previously obtained for von Neumann subalgebras and C*-subalgebras.


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


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 46L10

Retrieve articles in all journals with MSC (2000): 46L10


Additional Information

Jon Kraus
Affiliation: Department of Mathematics, State University of New York at Buffalo, Buffalo, New York 14260-2900
Email: mthjek@acsu.buffalo.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-03-07243-5
PII: S 0002-9939(03)07243-5
Received by editor(s): June 14, 2002
Received by editor(s) in revised form: December 13, 2002
Published electronically: November 4, 2003
Communicated by: David R. Larson
Article copyright: © Copyright 2003 American Mathematical Society