### Abstract

Let Y be a Hausdorff topological space, let V be a system of weights on Y, and let LVq(Y) and LVb(Y) be the weighted locally convex spaces of cross-sections with a topology generated by seminorms which are weighted analogues of the supremum norm. In the present paper, we characterise the multiplication operators on the spaces LV0(Y) and LVb(Y) induced by the scalar-valued, the vector-valued, and the operator-valued mappings. A (linear) dynamical system on the weighted spaces of cross-sections is obtained as an application of the theory of the multiplication operators. Many examples are given to illustrate the theory.

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

Pages (from-to) | 547-554 |

Number of pages | 8 |

Journal | Proceedings of the American Mathematical Society |

Volume | 119 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1993 |

### Fingerprint

### Keywords

- Cross-sections
- Dynamical systems
- Multiplication operators
- Seminorms
- Vector-valued and operator-valued mappings
- Weights

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

**Multiplicationo perators and dynamicals ystems on weighted spaces of cross-sections.** / Singh, R. K.; Manhas, J. S.

Research output: Contribution to journal › Article

*Proceedings of the American Mathematical Society*, vol. 119, no. 2, pp. 547-554. https://doi.org/10.1090/S0002-9939-1993-1155602-0

}

TY - JOUR

T1 - Multiplicationo perators and dynamicals ystems on weighted spaces of cross-sections

AU - Singh, R. K.

AU - Manhas, J. S.

PY - 1993

Y1 - 1993

N2 - Let Y be a Hausdorff topological space, let V be a system of weights on Y, and let LVq(Y) and LVb(Y) be the weighted locally convex spaces of cross-sections with a topology generated by seminorms which are weighted analogues of the supremum norm. In the present paper, we characterise the multiplication operators on the spaces LV0(Y) and LVb(Y) induced by the scalar-valued, the vector-valued, and the operator-valued mappings. A (linear) dynamical system on the weighted spaces of cross-sections is obtained as an application of the theory of the multiplication operators. Many examples are given to illustrate the theory.

AB - Let Y be a Hausdorff topological space, let V be a system of weights on Y, and let LVq(Y) and LVb(Y) be the weighted locally convex spaces of cross-sections with a topology generated by seminorms which are weighted analogues of the supremum norm. In the present paper, we characterise the multiplication operators on the spaces LV0(Y) and LVb(Y) induced by the scalar-valued, the vector-valued, and the operator-valued mappings. A (linear) dynamical system on the weighted spaces of cross-sections is obtained as an application of the theory of the multiplication operators. Many examples are given to illustrate the theory.

KW - Cross-sections

KW - Dynamical systems

KW - Multiplication operators

KW - Seminorms

KW - Vector-valued and operator-valued mappings

KW - Weights

UR - http://www.scopus.com/inward/record.url?scp=84966243823&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84966243823&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-1993-1155602-0

DO - 10.1090/S0002-9939-1993-1155602-0

M3 - Article

VL - 119

SP - 547

EP - 554

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 2

ER -