### Abstract

If V is a system of weights on a completely regular Hausdorff space X and E is a locally convex space, then CV_{Q}(X, E) and CV_{b}(X, E) are locally convex spaces of vector-valued continuous functions with topologies generated by seminorms which are weighted analogues of the supremum norm. In this paper we characterise multiplication operators on these spaces induced by scalar-valued and vector-valued mappings. Many examples are presented to illustrate the theory.

Original language | English |
---|---|

Pages (from-to) | 98-107 |

Number of pages | 10 |

Journal | Journal of the Australian Mathematical Society |

Volume | 50 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1991 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

**Multiplication Operators on Weighted Spaces of Vector-Valued Continuous Functions.** / Singh, R. K.; Manhas, JAsbir Singh.

Research output: Contribution to journal › Article

*Journal of the Australian Mathematical Society*, vol. 50, no. 1, pp. 98-107. https://doi.org/10.1017/S1446788700032584

}

TY - JOUR

T1 - Multiplication Operators on Weighted Spaces of Vector-Valued Continuous Functions

AU - Singh, R. K.

AU - Manhas, JAsbir Singh

PY - 1991

Y1 - 1991

N2 - If V is a system of weights on a completely regular Hausdorff space X and E is a locally convex space, then CVQ(X, E) and CVb(X, E) are locally convex spaces of vector-valued continuous functions with topologies generated by seminorms which are weighted analogues of the supremum norm. In this paper we characterise multiplication operators on these spaces induced by scalar-valued and vector-valued mappings. Many examples are presented to illustrate the theory.

AB - If V is a system of weights on a completely regular Hausdorff space X and E is a locally convex space, then CVQ(X, E) and CVb(X, E) are locally convex spaces of vector-valued continuous functions with topologies generated by seminorms which are weighted analogues of the supremum norm. In this paper we characterise multiplication operators on these spaces induced by scalar-valued and vector-valued mappings. Many examples are presented to illustrate the theory.

UR - http://www.scopus.com/inward/record.url?scp=0040061730&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0040061730&partnerID=8YFLogxK

U2 - 10.1017/S1446788700032584

DO - 10.1017/S1446788700032584

M3 - Article

AN - SCOPUS:0040061730

VL - 50

SP - 98

EP - 107

JO - Journal of the Australian Mathematical Society

JF - Journal of the Australian Mathematical Society

SN - 1446-7887

IS - 1

ER -