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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Strong martingale convergence of generalized conditional expectations on von Neumann algebras


Authors: Fumio Hiai and Makoto Tsukada
Journal: Trans. Amer. Math. Soc. 282 (1984), 791-798
MSC: Primary 46L50
DOI: https://doi.org/10.1090/S0002-9947-1984-0732120-1
MathSciNet review: 732120
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Abstract: Accardi and Cecchini generalized the concept of conditional expectations on von Neumann algebras. In this paper we give some conditions for strong convergence of increasing or decreasing martingales of Accardi and Cecchini's conditional expectations.


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DOI: https://doi.org/10.1090/S0002-9947-1984-0732120-1
Keywords: Conditional expectation, martingale, Tomita-Takesaki theory, faithful normal semifinite weight, nonabelian $ K$-flow
Article copyright: © Copyright 1984 American Mathematical Society