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http://dx.doi.org/10.4134/JKMS.2008.45.5.1203

WEIGHTED COMPOSITION OPERATORS ON WEIGHTED SPACES OF VECTOR-VALUED ANALYTIC FUNCTIONS  

Manhas, Jasbir Singh (Department of Mathematics and Statistics College of Science, Sultan Qaboos University)
Publication Information
Journal of the Korean Mathematical Society / v.45, no.5, 2008 , pp. 1203-1220 More about this Journal
Abstract
Let V be an arbitrary system of weights on an open connected subset G of ${\mathbb{C}}^N(N{\geq}1)$ and let B (E) be the Banach algebra of all bounded linear operators on a Banach space E. Let $HV_b$ (G, E) and $HV_0$ (G, E) 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 ${\Psi}:G{\rightarrow}B(E)$ 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.
Keywords
system of weights; Banach algebra; weighted locally convex spaces of vector-valued analytic functions; weighted composition operators; invertible and compact operators;
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