### Abstract

Let B_{X} and B_{Y} be the open unit balls of the Banach Spaces X and Y , respectively. Let V and W be two countable families of weights on B_{X} and B_{Y} , respectively. Let HV (B_{X}) (or HV_{0} (B_{X})) and HW (B_{Y}) (or HW_{0} (B_{Y})) be the weighted Fréchet spaces of holomorphic functions. In this paper, we investigate the holomorphic mappings φ : B_{X} → B_{Y} and Ψ: B_{X} → C which characterize continuous weighted composition operators between the spaces HV (B_{X}) (or HV_{0} (B_{X})) and HW (B_{Y}) (or HW_{0} (B_{Y})) : Also, we obtained a (linear) dynamical system induced by multiplication operators on these weighted spaces.

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

Pages (from-to) | 58-71 |

Number of pages | 14 |

Journal | Annals of Functional Analysis |

Volume | 4 |

Issue number | 2 |

Publication status | Published - 2013 |

### Fingerprint

### Keywords

- Dynamical system
- Multiplication operator.
- Weight
- Weighted composition operator
- Weighted frechet space

### ASJC Scopus subject areas

- Analysis
- Control and Optimization

### Cite this

**Weighted composition operators and dynamical systems on weighted spaces of holomorphic functions on banach spaces.** / Manhas, J. S.

Research output: Contribution to journal › Article

*Annals of Functional Analysis*, vol. 4, no. 2, pp. 58-71.

}

TY - JOUR

T1 - Weighted composition operators and dynamical systems on weighted spaces of holomorphic functions on banach spaces

AU - Manhas, J. S.

PY - 2013

Y1 - 2013

N2 - Let BX and BY be the open unit balls of the Banach Spaces X and Y , respectively. Let V and W be two countable families of weights on BX and BY , respectively. Let HV (BX) (or HV0 (BX)) and HW (BY) (or HW0 (BY)) be the weighted Fréchet spaces of holomorphic functions. In this paper, we investigate the holomorphic mappings φ : BX → BY and Ψ: BX → C which characterize continuous weighted composition operators between the spaces HV (BX) (or HV0 (BX)) and HW (BY) (or HW0 (BY)) : Also, we obtained a (linear) dynamical system induced by multiplication operators on these weighted spaces.

AB - Let BX and BY be the open unit balls of the Banach Spaces X and Y , respectively. Let V and W be two countable families of weights on BX and BY , respectively. Let HV (BX) (or HV0 (BX)) and HW (BY) (or HW0 (BY)) be the weighted Fréchet spaces of holomorphic functions. In this paper, we investigate the holomorphic mappings φ : BX → BY and Ψ: BX → C which characterize continuous weighted composition operators between the spaces HV (BX) (or HV0 (BX)) and HW (BY) (or HW0 (BY)) : Also, we obtained a (linear) dynamical system induced by multiplication operators on these weighted spaces.

KW - Dynamical system

KW - Multiplication operator.

KW - Weight

KW - Weighted composition operator

KW - Weighted frechet space

UR - http://www.scopus.com/inward/record.url?scp=84894551583&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84894551583&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:84894551583

VL - 4

SP - 58

EP - 71

JO - Annals of Functional Analysis

JF - Annals of Functional Analysis

SN - 2008-8752

IS - 2

ER -