### Abstract

Let U_{X} be a balanced open subset of a Banach space X. Let V and W be two Nachbin families of weights on U_{X}. Let B(E, F) be the space of all continuous linear operators from a locally convex Haudorff space E into a locally convex Hausdorff space F. Let HV (U_{X}, F) and HW (U_{X}, E) be the weighted locally convex spaces of vector-valued holomorphic functions. In this paper, we investigate the operator-valued maps ψ: U_{X} → B (E,F) which generate multiplication operators and invertible multiplication operators Mψ on the spaces HV (U_{X}, F) and HW (U_{X}, E) for general Nachbin families of weights V and W and for single continuous weights v and w on the open unit ball B_{X} of a Banach space X. A C_{0}-group of multiplication operators and a (linear) dynamical system is also obtained as an application of these operators.

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

Pages (from-to) | 1075-1086 |

Number of pages | 12 |

Journal | International Journal of Mathematical Analysis |

Volume | 5 |

Issue number | 21-24 |

Publication status | Published - 2011 |

### Fingerprint

### Keywords

- C-group
- Dynamical systems
- Invertible multiplication operators
- Multiplication operators
- Nachbin families
- Operated-valued holomorphic maps
- Vector-valued holomorphic maps
- Weighted locally convex spaces
- Weights

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

**Multiplication operators and dynamical systems on weighted spaces of vector-valued holomorphic functions on banach spaces.** / Manhas, J. S.

Research output: Contribution to journal › Article

*International Journal of Mathematical Analysis*, vol. 5, no. 21-24, pp. 1075-1086.

}

TY - JOUR

T1 - Multiplication operators and dynamical systems on weighted spaces of vector-valued holomorphic functions on banach spaces

AU - Manhas, J. S.

PY - 2011

Y1 - 2011

N2 - Let UX be a balanced open subset of a Banach space X. Let V and W be two Nachbin families of weights on UX. Let B(E, F) be the space of all continuous linear operators from a locally convex Haudorff space E into a locally convex Hausdorff space F. Let HV (UX, F) and HW (UX, E) be the weighted locally convex spaces of vector-valued holomorphic functions. In this paper, we investigate the operator-valued maps ψ: UX → B (E,F) which generate multiplication operators and invertible multiplication operators Mψ on the spaces HV (UX, F) and HW (UX, E) for general Nachbin families of weights V and W and for single continuous weights v and w on the open unit ball BX of a Banach space X. A C0-group of multiplication operators and a (linear) dynamical system is also obtained as an application of these operators.

AB - Let UX be a balanced open subset of a Banach space X. Let V and W be two Nachbin families of weights on UX. Let B(E, F) be the space of all continuous linear operators from a locally convex Haudorff space E into a locally convex Hausdorff space F. Let HV (UX, F) and HW (UX, E) be the weighted locally convex spaces of vector-valued holomorphic functions. In this paper, we investigate the operator-valued maps ψ: UX → B (E,F) which generate multiplication operators and invertible multiplication operators Mψ on the spaces HV (UX, F) and HW (UX, E) for general Nachbin families of weights V and W and for single continuous weights v and w on the open unit ball BX of a Banach space X. A C0-group of multiplication operators and a (linear) dynamical system is also obtained as an application of these operators.

KW - C-group

KW - Dynamical systems

KW - Invertible multiplication operators

KW - Multiplication operators

KW - Nachbin families

KW - Operated-valued holomorphic maps

KW - Vector-valued holomorphic maps

KW - Weighted locally convex spaces

KW - Weights

UR - http://www.scopus.com/inward/record.url?scp=80051595615&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=80051595615&partnerID=8YFLogxK

M3 - Article

VL - 5

SP - 1075

EP - 1086

JO - International Journal of Mathematical Analysis

JF - International Journal of Mathematical Analysis

SN - 1312-8876

IS - 21-24

ER -