TY - JOUR
T1 - Weighted composition operators on weighted spaces of vector-valued analytic functions
AU - Manhas, Jasbir Singh
PY - 2008/9
Y1 - 2008/9
N2 - 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.
AB - 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.
KW - Banach algebra
KW - Invertible and compact operators
KW - System of weights
KW - Weighted composition operators
KW - Weighted locally convex spaces of vector-valued analytic functions
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U2 - 10.4134/JKMS.2008.45.5.1203
DO - 10.4134/JKMS.2008.45.5.1203
M3 - Article
AN - SCOPUS:50949086144
SN - 0304-9914
VL - 45
SP - 1203
EP - 1220
JO - Journal of the Korean Mathematical Society
JF - Journal of the Korean Mathematical Society
IS - 5
ER -