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
DOI:
https://doi.org/10.1090/S0002-9939-99-05134-5
Published electronically:
July 28, 1999
MathSciNet review:
1641661
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: We show that a separable complex Banach space 
has the analytic Radon-Nikodym property if and only if there exists 
, such that the space consisting of all 
-bounded 
-valued analytic martingales is separable.
- 1. A. V. Bukhvalov and A. A. Danilevich, Boundary properties of analytic and harmonic functions with values in a Banach space, Mat. Zametki 31 (1982), no. 2, 203–214, 317 (Russian). MR 649004
- 2. G. A. Edgar, Analytic martingale convergence, J. Funct. Anal. 69 (1986), no. 2, 268–280. MR 865224, https://doi.org/10.1016/0022-1236(86)90092-3
- 3. N. Ghoussoub and B. Maurey, Plurisubharmonic martingales and barriers in complex quasi-Banach spaces, Ann. Inst. Fourier (Grenoble) 39 (1989), no. 4, 1007–1060 (English, with French summary). MR 1036341
- 4. N. Ghoussoub, J. Lindenstrauss, and B. Maurey, Analytic martingales and plurisubharmonic barriers in complex Banach spaces, Banach space theory (Iowa City, IA, 1987) Contemp. Math., vol. 85, Amer. Math. Soc., Providence, RI, 1989, pp. 111–130. MR 983384, https://doi.org/10.1090/conm/085/983384
- 5. Shang Quan Bu and Walter Schachermayer, Approximation of Jensen measures by image measures under holomorphic functions and applications, Trans. Amer. Math. Soc. 331 (1992), no. 2, 585–608. MR 1035999, https://doi.org/10.1090/S0002-9947-1992-1035999-6
- 6. Mohamed Daher, Une remarque sur la propriété de Radon-Nikodým, C. R. Acad. Sci. Paris Sér. I Math. 313 (1991), no. 5, 269–271 (French, with English summary). MR 1126393
- 7. B. J. H. Garling, On martingales with values in complex Banach spaces, Math. Pro. Phil. Soc., 104 (1988), 399-406.
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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
