### 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 |
---|---|

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.

**Weighted composition operators on nonlocally convex weighted spaces of continuous functions.** / Manhas, J. S.; Singh, R. K.

Research output: Contribution to journal › Article

*Analysis Mathematica*, vol. 24, no. 4, pp. 275-292.

}

TY - JOUR

T1 - Weighted composition operators on nonlocally convex weighted spaces of continuous functions

AU - Manhas, J. S.

AU - Singh, R. K.

PY - 1998

Y1 - 1998

N2 - 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 CV0(X, E) and CVb(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 Wπ, Φ on CV0(X, E) (or CVb(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.

AB - 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 CV0(X, E) and CVb(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 Wπ, Φ on CV0(X, E) (or CVb(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.

UR - http://www.scopus.com/inward/record.url?scp=27844467304&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=27844467304&partnerID=8YFLogxK

M3 - Article

VL - 24

SP - 275

EP - 292

JO - Analysis Mathematica

JF - Analysis Mathematica

SN - 0133-3852

IS - 4

ER -