## Abstract

The composition operator induced by a hyperbolic Möbius transform ϕ on the classical Hardy space H^{2} is considered. It is known that the invariant subspace problem for Hilbert space operators is equivalent to the fact that all the minimal invariant subspaces of this operator are one- dimensional. In connection with that we try to decide by the properties of a given function u in H^{2} if the corresponding cyclic subspace is minimal or not. The main result is the following. If the radial limit of u is continuously extendable at one of the fixed points of ϕ and its value at the point is nonzero, then the cyclic subspace generated by u is minimal if and only if u is constant.

Original language | English (US) |
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Pages (from-to) | 837-841 |

Number of pages | 5 |

Journal | Proceedings of the American Mathematical Society |

Volume | 119 |

Issue number | 3 |

DOIs | |

State | Published - Nov 1993 |

Externally published | Yes |

## ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics