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A new characterisation of the analytic Radon-Nikodym property


Author: Bu Shangquan
Journal: Proc. Amer. Math. Soc. 128 (2000), 1017-1022
MSC (1991): Primary 46B20
Published electronically: July 28, 1999
MathSciNet review: 1641661
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Abstract: We show that a separable complex Banach space $X$ has the analytic Radon-Nikodym property if and only if there exists $1\leq p <\infty $, such that the space consisting of all $L^{p}$-bounded $X$-valued analytic martingales is separable.


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Additional Information

Bu Shangquan
Affiliation: Department of Applied Mathematics, Tsinghua University, 100084 Beijing, People’s Republic of China
Email: sbu@math.tsinghua.edu.cn

DOI: https://doi.org/10.1090/S0002-9939-99-05134-5
Keywords: Analytic Radon-Nikodym property, analytic martingale, separable Banach spaces
Received by editor(s): May 14, 1998
Published electronically: July 28, 1999
Additional Notes: This research was supported by the Natural Sciences Foundation of China and the Fok Ying Tung Education Foundation
Communicated by: Dale Alspach
Article copyright: © Copyright 2000 American Mathematical Society