TY - JOUR
T1 - Multiplication operators and dynamical systems on weighted spaces of vector-valued holomorphic functions on banach spaces
AU - Manhas, J. S.
PY - 2011
Y1 - 2011
N2 - Let UX be a balanced open subset of a Banach space X. Let V and W be two Nachbin families of weights on UX. Let B(E, F) be the space of all continuous linear operators from a locally convex Haudorff space E into a locally convex Hausdorff space F. Let HV (UX, F) and HW (UX, E) be the weighted locally convex spaces of vector-valued holomorphic functions. In this paper, we investigate the operator-valued maps ψ: UX → B (E,F) which generate multiplication operators and invertible multiplication operators Mψ on the spaces HV (UX, F) and HW (UX, E) for general Nachbin families of weights V and W and for single continuous weights v and w on the open unit ball BX of a Banach space X. A C0-group of multiplication operators and a (linear) dynamical system is also obtained as an application of these operators.
AB - Let UX be a balanced open subset of a Banach space X. Let V and W be two Nachbin families of weights on UX. Let B(E, F) be the space of all continuous linear operators from a locally convex Haudorff space E into a locally convex Hausdorff space F. Let HV (UX, F) and HW (UX, E) be the weighted locally convex spaces of vector-valued holomorphic functions. In this paper, we investigate the operator-valued maps ψ: UX → B (E,F) which generate multiplication operators and invertible multiplication operators Mψ on the spaces HV (UX, F) and HW (UX, E) for general Nachbin families of weights V and W and for single continuous weights v and w on the open unit ball BX of a Banach space X. A C0-group of multiplication operators and a (linear) dynamical system is also obtained as an application of these operators.
KW - C-group
KW - Dynamical systems
KW - Invertible multiplication operators
KW - Multiplication operators
KW - Nachbin families
KW - Operated-valued holomorphic maps
KW - Vector-valued holomorphic maps
KW - Weighted locally convex spaces
KW - Weights
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M3 - Article
AN - SCOPUS:80051595615
SN - 1312-8876
VL - 5
SP - 1075
EP - 1086
JO - International Journal of Mathematical Analysis
JF - International Journal of Mathematical Analysis
IS - 21-24
ER -