The splitting problem for subspaces of tensor products of operator algebras
Author:
Jon Kraus
Journal:
Proc. Amer. Math. Soc. 132 (2004), 11251131
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 142602900
Email:
mthjek@acsu.buffalo.edu
DOI:
http://dx.doi.org/10.1090/S0002993903072435
PII:
S 00029939(03)072435
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
