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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Characterization of subdiagonal algebras


Author: Turdebek N. Bekjan
Journal: Proc. Amer. Math. Soc. 139 (2011), 1121-1126
MSC (2010): Primary 46L51, 46L52, 47L75
Published electronically: September 30, 2010
MathSciNet review: 2745664
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Abstract: Let $ \mathcal{M}$ be a finite von Neumann algebra with a faithful normal tracial state $ \tau,$ and let $ \mathcal{A}$ be a tracial subalgebra of $ \mathcal{M}.$ We show that $ \mathcal{A}$ has $ L^{p}$-factorization ( $ 1\leq p<\infty$) if and only if $ \mathcal{A}$ is a subdiagonal algebra. Also, we obtain some characterizations of subdiagonal algebras.


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Additional Information

Turdebek N. Bekjan
Affiliation: College of Mathematics and Systems Sciences, Xinjiang University, Urumqi 830046, People’s Republic of China

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10673-1
PII: S 0002-9939(2010)10673-1
Keywords: von Neumann algebras, tracial subalgebra, subdiagonal algebra, $L^{2}$-density, $L^{p}$-factorization
Received by editor(s): November 30, 2009
Received by editor(s) in revised form: April 13, 2010
Published electronically: September 30, 2010
Additional Notes: The author was partially supported by NSFC grant No. 10761009
Communicated by: Marius Junge
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.