Characterization of subdiagonal algebras
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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.References
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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
- MR Author ID: 627291
- 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
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 139 (2011), 1121-1126
- MSC (2010): Primary 46L51, 46L52, 47L75
- DOI: https://doi.org/10.1090/S0002-9939-2010-10673-1
- MathSciNet review: 2745664