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