## Abstract

A function/ in H∞ is said to be a weak-star generator (w*-gen.) of the function e_{n}(z) = z^{n}, \z\ < 1, n=, 1 if lim∝ p_{∝} ° f = e_{n} (w*-topology), for some net (p_{∝} of complex polynomials. For the case n = 1, f is called a w*- gen. of H^{∞} The w*-generators of H^{∞} have been defined and characterized by Sarason. It is the purpose of the present paper to give necessary and sufficient conditions for a function to generate e_{n}. As a result, it follows from our characterization that certain analytic Toeplitz operators have the transitive algebra property.

Original language | English (US) |
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Pages (from-to) | 131-136 |

Number of pages | 6 |

Journal | Proceedings of the American Mathematical Society |

Volume | 103 |

Issue number | 1 |

DOIs | |

State | Published - May 1988 |

## All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics

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