## 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 |
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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 |

## 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)