On maximal injective subalgebras

Author:
Mingchu Gao

Journal:
Proc. Amer. Math. Soc. **138** (2010), 2065-2070

MSC (2010):
Primary 46L10

Published electronically:
January 7, 2010

MathSciNet review:
2596043

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Abstract | References | Similar Articles | Additional Information

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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Additional Information

**Mingchu Gao**

Affiliation:
Department of Mathematics, Louisiana College, Pineville, Louisiana 71359

Email:
gao@lacollege.edu

DOI:
http://dx.doi.org/10.1090/S0002-9939-10-10219-6

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.