### 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) |
---|---|

Pages (from-to) | 131-136 |

Number of pages | 6 |

Journal | Proceedings of the American Mathematical Society |

Volume | 103 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 1988 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics

### Cite this

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**Weak-star generators of z ^{n}, n > 1, and transitive operator algebras.** / Ansari, Mohamad A.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Weak-star generators of zn, n > 1, and transitive operator algebras

AU - Ansari, Mohamad A.

PY - 1988/1/1

Y1 - 1988/1/1

N2 - A function/ in H∞ is said to be a weak-star generator (w*-gen.) of the function en(z) = zn, \z\ < 1, n=, 1 if lim∝ p∝ ° f = en (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 en. As a result, it follows from our characterization that certain analytic Toeplitz operators have the transitive algebra property.

AB - A function/ in H∞ is said to be a weak-star generator (w*-gen.) of the function en(z) = zn, \z\ < 1, n=, 1 if lim∝ p∝ ° f = en (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 en. As a result, it follows from our characterization that certain analytic Toeplitz operators have the transitive algebra property.

UR - http://www.scopus.com/inward/record.url?scp=84966207408&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84966207408&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-1988-0938656-1

DO - 10.1090/S0002-9939-1988-0938656-1

M3 - Article

AN - SCOPUS:84966207408

VL - 103

SP - 131

EP - 136

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 1

ER -