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.
|الصفحات (من إلى)||1075-1086|
|دورية||International Journal of Mathematical Analysis|
|حالة النشر||Published - 2011|
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