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

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Abstract: The main result of this paper is that if is a von Neumann algebra that is a factor and has the weak* operator approximation property (the weak* OAP), and if is a von Neumann algebra, then every -weakly closed subspace of that is an -bimodule (under multiplication) splits, in the sense that there is a -weakly closed subspace of such that . Note that if is a von Neumann subalgebra of , then is an -bimodule if and only if . So this result is a generalization (in the case where has the weak* OAP) of the result of Ge and Kadison that if is a factor, then every von Neumann subalgebra of that contains splits. We also obtain other results concerning the splitting of -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.

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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:
https://doi.org/10.1090/S0002-9939-03-07243-5

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