A noncommutative Szegö theorem for subdiagonal subalgebras of von Neumann algebras

Labuschagne, L.

doi:10.1090/S0002-9939-05-08064-0

A noncommutative Szegö theorem for subdiagonal subalgebras of von Neumann algebras
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by L. E. Labuschagne PDF

Proc. Amer. Math. Soc. 133 (2005), 3643-3646 Request permission

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.

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