### Abstract

We characterise the compact composition operators from any Mobius invariant Banach space to VMOA, the space of holomorphic functions on the unit disk U that have vanishing mean oscillation. We use this to obtain a characterisation of the compact composition operators from the Bloch space to VMOA. Finally, we study some properties of hyperbolic VMOA functions. We show that a function is hyperbolic VMOA if and only if it is the symbol of a compact composition operator from the Bloch space to VMOA.

Original language | English |
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Pages (from-to) | 1-19 |

Number of pages | 19 |

Journal | Bulletin of the Australian Mathematical Society |

Volume | 62 |

Issue number | 1 |

Publication status | Published - Aug 2000 |

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Makhmutov, S., & Tjani, M. (2000). Composition operators on some Möbius invariant Banach spaces.

*Bulletin of the Australian Mathematical Society*,*62*(1), 1-19.