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Proceedings of the American Mathematical Society

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

 

 

On the algebra of bounded holomorphic martingales


Author: Hitoshi Arai
Journal: Proc. Amer. Math. Soc. 97 (1986), 616-620
MSC: Primary 46J15; Secondary 60G46
DOI: https://doi.org/10.1090/S0002-9939-1986-0845975-4
MathSciNet review: 845975
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Abstract: The properties of the algebra $ {H^\infty }$ of bounded holomorphic martingales are further studied following the work of N. Th. Varopoulos [11]. The purpose of this paper is to discuss the behavior of weak* closed algebras $ B$ with $ {H^\infty }_ \ne ^ \subset B_ \ne ^ \subset {L^\infty }$ and the support sets of $ {H^\infty }$-functions. We also give some results on the factorization theorem for $ {H^\infty }$ and extreme points of the unit ball of $ {H^\infty }$.


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DOI: https://doi.org/10.1090/S0002-9939-1986-0845975-4
Keywords: Holomorphic martingales, weak* Dirichlet algebras, Hardy spaces
Article copyright: © Copyright 1986 American Mathematical Society