### Abstract

Let U_{X} be a balanced open subset of a Banach space X. Let V and W be two Nachbin families of weights on U_{X}. Let B(E, F) be the space of all continuous linear operators from a locally convex Haudorff space E into a locally convex Hausdorff space F. Let HV (U_{X}, F) and HW (U_{X}, E) be the weighted locally convex spaces of vector-valued holomorphic functions. In this paper, we investigate the operator-valued maps ψ: U_{X} → B (E,F) which generate multiplication operators and invertible multiplication operators Mψ on the spaces HV (U_{X}, F) and HW (U_{X}, E) for general Nachbin families of weights V and W and for single continuous weights v and w on the open unit ball B_{X} of a Banach space X. A C_{0}-group of multiplication operators and a (linear) dynamical system is also obtained as an application of these operators.

Original language | English |
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Pages (from-to) | 1075-1086 |

Number of pages | 12 |

Journal | International Journal of Mathematical Analysis |

Volume | 5 |

Issue number | 21-24 |

Publication status | Published - 2011 |

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### Keywords

- C-group
- Dynamical systems
- Invertible multiplication operators
- Multiplication operators
- Nachbin families
- Operated-valued holomorphic maps
- Vector-valued holomorphic maps
- Weighted locally convex spaces
- Weights

### ASJC Scopus subject areas

- Mathematics(all)