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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

The strong limit of von Neumann subalgebras with conditional expectations


Author: Makoto Tsukada
Journal: Proc. Amer. Math. Soc. 94 (1985), 259-264
MSC: Primary 46L50; Secondary 46L10, 46L30
DOI: https://doi.org/10.1090/S0002-9939-1985-0784175-2
MathSciNet review: 784175
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Abstract: The strong lower limit and the weak upper limit of a net of von Neumann subalgebras on which the conditional expectations exist with respect to a fixed faithful normal state are defined. The limits coincide if and only if the corresponding conditional expectations converge strongly.


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DOI: https://doi.org/10.1090/S0002-9939-1985-0784175-2
Keywords: Faithful normal state, conditional expectation, martingale
Article copyright: © Copyright 1985 American Mathematical Society