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On martingales with values in a complex Banach space

Published online by Cambridge University Press:  24 October 2008

D. J. H. Garling
D. J. H. Garling
Affiliation:
St John's College, Cambridge
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Extract

In recent years it has become clear that there are several ways in which complex Banach spaces can differ quite markedly from their real counterparts, and many of these concern martingales. Thus, in [6] complex uniform convexity was related to martingale inequalities, in [3] and [7] the convergence of L1-bounded analytic martingales was considered and in [8] this property was related to the analytic Radon–Nikodym property.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 104 , Issue 2 , September 1988 , pp. 399 - 406
Copyright
Copyright © Cambridge Philosophical Society 1988

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References

REFERENCES

[1]Aldous, D. J.. Unconditional bases and martingales in Lp(F). Math. Proc. Cambridge Philos. Soc. 85 (1979), 117–123.CrossRefGoogle Scholar
[2]Bourgain, J.. Some remarks on Banach spaces in which martingale difference sequences are unconditional. Ark. Mat. 14 (1983), 163–168.CrossRefGoogle Scholar
[3]Bourgain, J. and Davis, W. J.. Martingale transforms and complex uniform convexity. (To appear.)Google Scholar
[4]Bukhvalov, A. V. and Danilevich, A. A.. Boundary properties of analytic and harmonic functions with values in Banach space. Mat. Zametki 31 (1982) 203–214Google Scholar
English translation Math. Notes 31 (1982), 104–110.CrossRefGoogle Scholar
[5]Burkholder, D. L.. A geometrical characterization of Banach spaces in which martingale difference sequences are unconditional. Ann. Probab. 9 (1981), 997–1011.Google Scholar
[6]Davis, W. J., Garling, D. J. H. and Tomczak-Jaegermann, N.. The complex convexity of quasi-normed linear spaces. J. Fund. Anal. 55 (1984) 110–150.CrossRefGoogle Scholar
[7]Edgar, G. A.. Complex martingale convergence. In Banach spaces, Lecture Notes in Math. vol. 1166 (Springer-Verlag 1985), pp. 38–59.CrossRefGoogle Scholar
[8]Edgar, G. A.. Analytic martingale convergence. J. Fund. Anal., to appear.Google Scholar
[9]Garsia, A.. Martingale Inequalities: Seminar Notes on Recent Progress (Benjamin, 1973).Google Scholar
[10]Kwapień, S.. On Banach spaces containing c 0. Studia Math. 52 (1974), 187–188.CrossRefGoogle Scholar
[11]Maurey, B. and Pisier, G.. Séries de variables aléatoires vectorielles indépendantes et propriétés géometriques des espaces de Banach. Studia Math. 58 (1976), 45–90.CrossRefGoogle Scholar
[12]Meyer, P. A.. Martingales and Stochastic Integrals 1. Lecture Notes in Math. vol. 284 (Springer-Verlag, 1976).Google Scholar