### Abstract

Let B(E, F) be the Banach Space of all continuous linear operators from a Banach Space E into a Banach space F. Let U_{X} and U_{Y} be balanced open subsets of Banach spaces X and Y, respectively. Let V and W be two Nachbin families of continuous weights on U_{X} and U_{Y}, respectively. Let HV(U_{X}, E) (or HV_{0}(U_{X}, E)) and HW(U_{Y}, F) (or HW_{0}(U_{Y}, F)) be the weighted spaces of vector-valued holomorphic functions. In this paper, we investigate the holomorphic mappings φ: U_{Y} → U_{X} and ψ: U_{Y} → B(E, F) which generate weighted composition operators between these weighted spaces.

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

Pages (from-to) | 929-934 |

Number of pages | 6 |

Journal | Applied Mathematics and Computation |

Volume | 218 |

Issue number | 3 |

DOIs | |

Publication status | Published - Oct 1 2011 |

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### Keywords

- Nachbin families
- Vector-valued holomorphic functions
- Weighted composition operators
- Weighted spaces
- Weights

### ASJC Scopus subject areas

- Applied Mathematics
- Computational Mathematics

### Cite this

**Weighted composition operators between weighted spaces of vector-valued holomorphic functions on Banach spaces.** / Manhas, J. S.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Weighted composition operators between weighted spaces of vector-valued holomorphic functions on Banach spaces

AU - Manhas, J. S.

PY - 2011/10/1

Y1 - 2011/10/1

N2 - Let B(E, F) be the Banach Space of all continuous linear operators from a Banach Space E into a Banach space F. Let UX and UY be balanced open subsets of Banach spaces X and Y, respectively. Let V and W be two Nachbin families of continuous weights on UX and UY, respectively. Let HV(UX, E) (or HV0(UX, E)) and HW(UY, F) (or HW0(UY, F)) be the weighted spaces of vector-valued holomorphic functions. In this paper, we investigate the holomorphic mappings φ: UY → UX and ψ: UY → B(E, F) which generate weighted composition operators between these weighted spaces.

AB - Let B(E, F) be the Banach Space of all continuous linear operators from a Banach Space E into a Banach space F. Let UX and UY be balanced open subsets of Banach spaces X and Y, respectively. Let V and W be two Nachbin families of continuous weights on UX and UY, respectively. Let HV(UX, E) (or HV0(UX, E)) and HW(UY, F) (or HW0(UY, F)) be the weighted spaces of vector-valued holomorphic functions. In this paper, we investigate the holomorphic mappings φ: UY → UX and ψ: UY → B(E, F) which generate weighted composition operators between these weighted spaces.

KW - Nachbin families

KW - Vector-valued holomorphic functions

KW - Weighted composition operators

KW - Weighted spaces

KW - Weights

UR - http://www.scopus.com/inward/record.url?scp=80052265039&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=80052265039&partnerID=8YFLogxK

U2 - 10.1016/j.amc.2011.03.131

DO - 10.1016/j.amc.2011.03.131

M3 - Article

VL - 218

SP - 929

EP - 934

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

SN - 0096-3003

IS - 3

ER -