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ISSN 1088-6826(e) ISSN 0002-9939(p)

A noncommutative Szegö theorem for subdiagonal subalgebras of von Neumann algebras

Author(s): L. E. Labuschagne
Journal: Proc. Amer. Math. Soc. 133 (2005), 3643-3646.
MSC (2000): Primary 46L52; Secondary 46E25, 46J15
Posted: June 2, 2005
MathSciNet review: 2163602
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Abstract | References | Similar articles | Additional information

Abstract: For almost forty years now the most frustrating open problem regarding the theory of finite maximal subdiagonal algebras has been the question regarding the universal validity of a non-commutative Szegö theorem and Jensen inequality (Arveson, 1967). These two properties are known to be equivalent. Despite extensive efforts by many authors, their validity has to date only been established in some very special cases. In the present note we solve the general problem in the affirmative by proving the universal validity of Szegö's theorem for finite maximal subdiagonal algebras.

References:

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[E]: R. Exel, Maximal subdiagonal algebras, Amer. J. Math. 110(1988), 775 - 782. MR 0955297 (90b:46114)
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[R]: W. Rudin, Principles of mathematical analysis: 3rd edition, McGraw-Hill, 1976. MR 0385023 (52:5893)

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Additional Information:

L. E. Labuschagne
Affiliation: Department of Mathematical Sciences, University of South Africa, Box 392, 0003 Unisa, South Africa
Email: labusle@unisa.ac.za

DOI: 10.1090/S0002-9939-05-08064-0
PII: S 0002-9939(05)08064-0
Keywords: Subdiagonal algebra, non-commutative, Szeg\"{o}'s theorem, Jensen's inequality
Received by editor(s): August 18, 2004
Posted: June 2, 2005
Additional Notes: Part of this research was conducted with the support of a grant under the Poland -- South Africa cooperation agreement
Communicated by: David R. Larson
Copyright of article: Copyright 2005, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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