Mojahedi Mojtaba and Sady Fereshteh:
*Isometries on certain non-complete vector-valued function spaces.*
In: Acta scientiarum mathematicarum, (85) 3-4.
pp. 613-627. (2019)

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## Abstract

Surjective, not necessarily linear isometries T: AC(X, E)→AC(Y, F) between vector-valued absolutely continuous functions on compact subsets X and Y of the real line have recently been described as generalized weighted composition operators. The target spaces E and F are strictly convex normedspaces. In this paper, we assume that X and Y are compact Hausdorff spaces and E and F are normed spaces, which are not assumed to be strictly convex. We describe (with a short proof) surjective isometries T:(A,‖·‖A)→(B,‖·‖B) between certain normed subspaces A and B of C(X, E)and C(Y, F), respectively. We consider three cases for F with some mild conditions. The first case, in particular, provides a short proof for the above result, without assuming that the target spaces are strictly convex. The other cases give some generalizations in this topic. As a consequence, the results can be applied, for isometries (notnecessarily linear) between spaces of absolutely continuous vector-valued func-tions, (little) Lipschitz functions and also continuously differentiable functions.

Item Type: | Article |
---|---|

Journal or Publication Title: | Acta scientiarum mathematicarum |

Date: | 2019 |

Volume: | 85 |

Number: | 3-4 |

ISSN: | 2064-8316 |

Page Range: | pp. 613-627 |

Related URLs: | http://acta.bibl.u-szeged.hu/66425/ |

DOI: | 10.14232/actasm-018-092-6 |

Uncontrolled Keywords: | Valós lineáris izometriák, vektor-értékű függvényterek |

Additional Information: | Bibliogr.: p. 626-627. |

Date Deposited: | 2020. Apr. 23. 14:06 |

Last Modified: | 2021. Mar. 25. 15:34 |

URI: | http://acta.bibl.u-szeged.hu/id/eprint/66336 |

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