On maximal injective subalgebras
Author:
Mingchu Gao
Journal:
Proc. Amer. Math. Soc. 138 (2010), 20652070
MSC (2010):
Primary 46L10
Published electronically:
January 7, 2010
MathSciNet review:
2596043
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Abstract: Let be a type von Neumann subalgebra in a type factor with the faithful trace such that , for . Moreover, suppose has the asymptotically orthogonal property in after tensoring the finite von Neumann algebra , for all . Then we show that is maximal injective in the infinite tensor product von Neumann algebra . As a consequence, we get the following result. Let be a sequence of free groups with () generators. Let be the masa of group von Neumann algebra generated by a generator of or by the sum of all generators and their inverses of the group. Then is maximal injective in the infinite tensor product von Neumann algebra .
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 J. Fang. On maximal injective subalgebras of tensor products of von Neumann algebras. J. Funct. Anal., 244(1): 277288, 2007. MR 2294484 (2008d:46080)
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 L. Ge. On `Problems on von Neumann algebras by R. Kadison, 1967'. Acta Math. Sinica, English Series, 19(3): 619624, 2003. MR 2014042 (2005a:46120)
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 L. Ge and R. Kadison. On tensor products for von Neumann algebras. Invent. Math., 123(3): 453466, 1996. MR 1383957 (97c:46074)
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 C. Hou. On maximal injective subalgebras in a factor. Science in China Series A: Mathematics, 51: 20892096, 2008. MR 2447433 (2009i:46114)
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 R. Kadison. Problems on von Neumann algebras. Notes of Baton Rouge Conference, unpublished, 1967.
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 S. Popa. Maximal injective subalgebras in factors associated with free groups. Adv. Math., 50: 2748, 1983. MR 720738 (85h:46084)
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Additional Information
Mingchu Gao
Affiliation:
Department of Mathematics, Louisiana College, Pineville, Louisiana 71359
Email:
gao@lacollege.edu
DOI:
http://dx.doi.org/10.1090/S0002993910102196
Keywords:
Finite von Neumann algebras,
maximal injective subalgebras,
tensor products,
free group von Neumann algebras.
Received by editor(s):
March 16, 2009
Received by editor(s) in revised form:
September 20, 2009
Published electronically:
January 7, 2010
Communicated by:
Marius Junge
Article copyright:
© Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
