### Abstract

The properties of the algebra H∞ 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^{∞}⫋ B ⫋ L^{∞}and the support sets of H^{∞}-functions. We also give some results on the factorization theorem for H^{∞}and extreme points of the unit ball of H^{∞}.

Original language | English |
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Pages (from-to) | 616-620 |

Number of pages | 5 |

Journal | Proceedings of the American Mathematical Society |

Volume | 97 |

Issue number | 4 |

DOIs | |

Publication status | Published - 1986 Jan 1 |

### Fingerprint

### Keywords

- Hardy spaces
- Holomorphic martingales
- Weak* Dirichlet algebras

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

**On the algebra of bounded holomorphic martingales.** / Arai, Hitoshi.

Research output: Contribution to journal › Article

*Proceedings of the American Mathematical Society*, vol. 97, no. 4, pp. 616-620. https://doi.org/10.1090/S0002-9939-1986-0845975-4

}

TY - JOUR

T1 - On the algebra of bounded holomorphic martingales

AU - Arai, Hitoshi

PY - 1986/1/1

Y1 - 1986/1/1

N2 - The properties of the algebra H∞ 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∞⫋ B ⫋ L∞and the support sets of H∞-functions. We also give some results on the factorization theorem for H∞and extreme points of the unit ball of H∞.

AB - The properties of the algebra H∞ 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∞⫋ B ⫋ L∞and the support sets of H∞-functions. We also give some results on the factorization theorem for H∞and extreme points of the unit ball of H∞.

KW - Hardy spaces

KW - Holomorphic martingales

KW - Weak Dirichlet algebras

UR - http://www.scopus.com/inward/record.url?scp=84933771020&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84933771020&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-1986-0845975-4

DO - 10.1090/S0002-9939-1986-0845975-4

M3 - Article

AN - SCOPUS:84933771020

VL - 97

SP - 616

EP - 620

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 4

ER -