## Abstract

Let E and F be complex Banach spaces. We say that a holomorphic mapping f from E into F is compact respectively bounding if f maps some neighbourhood of every point of E into a relatively compact respectively bounding subset of F. Recall that a subset of E is bounding if it is mapped onto a bounded set by every complex valued holomorphic mapping on E. Compact holomorphic mappings have been studied by R. Aron and M. Schottenloher in [1]. Since every relatively compact subset of a Banach space is trivially bounding it is clear that every compact holomorphic mapping is bounding. We show that the product of three bounding holomorphic mappings is compact.

Original language | English |
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Pages (from-to) | 356-361 |

Number of pages | 6 |

Journal | Proceedings of the American Mathematical Society |

Volume | 105 |

Issue number | 2 |

DOIs | |

Publication status | Published - Feb 1989 |

MoE publication type | A1 Journal article-refereed |