Multiplication operators and dynamical systems on weighted spaces of vector-valued holomorphic functions on Banach spaces (Q2901458)

This paper generalizes previous results proved by the author in [Southeast Asian Bull. Math. 27, No. 4, 649--660 (2003; Zbl 1057.47038)]. Here, the author considers weighted spaces of holomorphic functions defined on (open subsets of) a Banach space. These spaces of weighted holomorphic functions defined on infinite dimensional Banach spaces were introduced by the reviewer [Quaest. Math. 19, No. 1--2, 341--352 (1996; Zbl 0858.46036)]. The author studies and characterizes multiplication operators between weighted spaces of holomorphic functions defined on balanced open subsets of a Banach space and with values on locally convex spaces. Invertible multiplication operators are also characterized. A \(C_0\)-group of multiplication operators and a (linear) dynamical system is also obtained as an application of these operators.