### Abstract

Let V be an arbitrary system of weights on an open connected subset G of ℂ^{N} (N≥ 1) and let B (E) be the Banach algebra of all bounded linear operators on a Banach space E. Let HV_{b} (G, E) and HVo (G, E) be the weighted locally convex spaces of vector-valued analytic functions. In this paper, we characterize self-analytic mappings φ : G → G and operator-valued analytic mappings ψ:G→B (E) which generate weighted composition operators and invertible weighted composition operators on the spaces HV_{b} (G, E) and HV_{0} (G, E) for different systems of weights V on G. Also, we obtained compact weighted composition operators on these spaces for some nice classes of weights.

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

Pages (from-to) | 1203-1220 |

Number of pages | 18 |

Journal | Journal of the Korean Mathematical Society |

Volume | 45 |

Issue number | 5 |

Publication status | Published - Sep 2008 |

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### Keywords

- Banach algebra
- Invertible and compact operators
- System of weights
- Weighted composition operators
- Weighted locally convex spaces of vector-valued analytic functions

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

**Weighted composition operators on weighted spaces of vector-valued analytic functions.** / Manhas, Jasbir Singh.

Research output: Contribution to journal › Article

*Journal of the Korean Mathematical Society*, vol. 45, no. 5, pp. 1203-1220.

}

TY - JOUR

T1 - Weighted composition operators on weighted spaces of vector-valued analytic functions

AU - Manhas, Jasbir Singh

PY - 2008/9

Y1 - 2008/9

N2 - Let V be an arbitrary system of weights on an open connected subset G of ℂN (N≥ 1) and let B (E) be the Banach algebra of all bounded linear operators on a Banach space E. Let HVb (G, E) and HVo (G, E) be the weighted locally convex spaces of vector-valued analytic functions. In this paper, we characterize self-analytic mappings φ : G → G and operator-valued analytic mappings ψ:G→B (E) which generate weighted composition operators and invertible weighted composition operators on the spaces HVb (G, E) and HV0 (G, E) for different systems of weights V on G. Also, we obtained compact weighted composition operators on these spaces for some nice classes of weights.

AB - Let V be an arbitrary system of weights on an open connected subset G of ℂN (N≥ 1) and let B (E) be the Banach algebra of all bounded linear operators on a Banach space E. Let HVb (G, E) and HVo (G, E) be the weighted locally convex spaces of vector-valued analytic functions. In this paper, we characterize self-analytic mappings φ : G → G and operator-valued analytic mappings ψ:G→B (E) which generate weighted composition operators and invertible weighted composition operators on the spaces HVb (G, E) and HV0 (G, E) for different systems of weights V on G. Also, we obtained compact weighted composition operators on these spaces for some nice classes of weights.

KW - Banach algebra

KW - Invertible and compact operators

KW - System of weights

KW - Weighted composition operators

KW - Weighted locally convex spaces of vector-valued analytic functions

UR - http://www.scopus.com/inward/record.url?scp=50949086144&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=50949086144&partnerID=8YFLogxK

M3 - Article

VL - 45

SP - 1203

EP - 1220

JO - Journal of the Korean Mathematical Society

JF - Journal of the Korean Mathematical Society

SN - 0304-9914

IS - 5

ER -