### Abstract

Let X be a completely regular Hausdorff space, let V be a system of weights on X and let E be a locally convex Hausdorff space. Let CV_{0}(X, E) and CV_{b}(X, E) be the weighted locally convex spaces of vector‐valued continuous functions with a topology generated by seminorms which are weighted analogue of the supremum norm. In the present paper, we characterize multiplication operators and weighted composition operators on the spaces CV_{0}(X, E) and CV_{b}(X, E) induced by scalar‐valued and vector‐valued mappings. A (linear) dynamical system on these weighted spaces is obtained as an application of the theory of multiplication operators.

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

Pages (from-to) | 279-285 |

Number of pages | 7 |

Journal | Mathematische Nachrichten |

Volume | 169 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1994 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Mathematische Nachrichten*,

*169*(1), 279-285. https://doi.org/10.1002/mana.19941690120

**Operators and Dynamical Systems on Weighted Function Spaces.** / Singh, R. K.; Manhas, J. S.

Research output: Contribution to journal › Article

*Mathematische Nachrichten*, vol. 169, no. 1, pp. 279-285. https://doi.org/10.1002/mana.19941690120

}

TY - JOUR

T1 - Operators and Dynamical Systems on Weighted Function Spaces

AU - Singh, R. K.

AU - Manhas, J. S.

PY - 1994

Y1 - 1994

N2 - Let X be a completely regular Hausdorff space, let V be a system of weights on X and let E be a locally convex Hausdorff space. Let CV0(X, E) and CVb(X, E) be the weighted locally convex spaces of vector‐valued continuous functions with a topology generated by seminorms which are weighted analogue of the supremum norm. In the present paper, we characterize multiplication operators and weighted composition operators on the spaces CV0(X, E) and CVb(X, E) induced by scalar‐valued and vector‐valued mappings. A (linear) dynamical system on these weighted spaces is obtained as an application of the theory of multiplication operators.

AB - Let X be a completely regular Hausdorff space, let V be a system of weights on X and let E be a locally convex Hausdorff space. Let CV0(X, E) and CVb(X, E) be the weighted locally convex spaces of vector‐valued continuous functions with a topology generated by seminorms which are weighted analogue of the supremum norm. In the present paper, we characterize multiplication operators and weighted composition operators on the spaces CV0(X, E) and CVb(X, E) induced by scalar‐valued and vector‐valued mappings. A (linear) dynamical system on these weighted spaces is obtained as an application of the theory of multiplication operators.

UR - http://www.scopus.com/inward/record.url?scp=84985335867&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84985335867&partnerID=8YFLogxK

U2 - 10.1002/mana.19941690120

DO - 10.1002/mana.19941690120

M3 - Article

AN - SCOPUS:84985335867

VL - 169

SP - 279

EP - 285

JO - Mathematische Nachrichten

JF - Mathematische Nachrichten

SN - 0025-584X

IS - 1

ER -