### Abstract

Let V be a system of weights on a completely regular Hausdorff space X and let B(E) be the topological vector space of all continuous linear operators on a general topological vector space E. Let CV_{0}(X, E) and CV_{b}(X, E) be the weighted spaces of vector-valued continuous functions (vanishing at infinity or bounded, respectively) which are not necessarily locally convex. In the present paper, we characterize in this general setting the weighted composition operators W_{π, Φ} on CV_{0}(X, E) (or CV_{b}(X, E)) induced by the operator-valued mappings π : X → B(E) (or the vector-valued mappings π : X → E, where E is a topological algebra) and the self-map Φ of X. Also, we characterize the mappings π : X → B(E) (or π : x → E) and π : X → X which induce the compact weighted composition operators on these weighted spaces of continuous functions.

Original language | English |
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Pages (from-to) | 275-292 |

Number of pages | 18 |

Journal | Analysis Mathematica |

Volume | 24 |

Issue number | 4 |

Publication status | Published - 1998 |

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### ASJC Scopus subject areas

- Applied Mathematics
- Analysis

### Cite this

*Analysis Mathematica*,

*24*(4), 275-292.