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

Title & Authors
WEIGHTED COMPOSITION OPERATORS ON WEIGHTED SPACES OF VECTOR-VALUED ANALYTIC FUNCTIONS
Manhas, Jasbir Singh;

Abstract
Let V be an arbitrary system of weights on an open connected subset G of $\small{{\mathbb{C}}^N(N{\geq}1)}$ and let B (E) be the Banach algebra of all bounded linear operators on a Banach space E. Let $\small{HV_b}$ (G, E) and $\small{HV_0}$ (G, E) be the weighted locally convex spaces of vector-valued analytic functions. In this paper, we characterize self-analytic mappings $\small{{\phi}:G{\rightarrow}G}$ and operator-valued analytic mappings $\small{{\Psi}:G{\rightarrow}B(E)}$ which generate weighted composition operators and invertible weighted composition operators on the spaces $\small{HV_b}$ (G, E) and $\small{HV_0}$ (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;
Language
English
Cited by
1.
Weighted composition operators between weighted spaces of vector-valued holomorphic functions on Banach spaces, Applied Mathematics and Computation, 2011, 218, 3, 929
2.
Tensor sum and dynamical systems, Acta Mathematica Scientia, 2014, 34, 6, 1935
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