Journal of the
Korean Mathematical Society JKMS

Let $V$ be an arbitrary system of weights on an open connected subset $G$ of $\mathbb{C}^{N}\left( N\geq1\right) $ and let $B\left( E\right) $ be the Banach algebra of all bounded linear operators on a Banach space $E$. Let $HV_{b}\left( G,E\right) $ and $HV_{0}\left( G,E\right) $ be the weighted locally convex spaces of vector-valued analytic functions. In this paper, we characterize self-analytic mappings $\phi:G\rightarrow G$ and operator-valued analytic mappings $\Psi:G\rightarrow B\left( E\right) $ which generate weighted composition operators and invertible weighted composition operators on the spaces $HV_{b}\left( G,E\right) $ and $HV_{0}\left( G,E\right) $ for different systems of weights $V$ on $G$. Also, we obtained compact weighted composition operators on these spaces for some nice classes of weights.

Keywords: system of weights, Banach algebra, weighted locally convex spaces of vector-valued analytic functions, weighted composition operators, invertible and compact operators

MSC numbers: Primary 47B37, 47B38, 47B07, 46E40, 46E10; Secondary 47D03, 37B05, 32A10, 30H05