Weighted Composition Operators and Dynamical Systems on Weighted Spaces of Holomorphic Functions on Banach Spaces

Let BX and BY be the open unit balls of the Banach SpacesX and Y , respectively. Let V and W be two countable families of weights on BX and BY , respectively. Let HV (BX) (or HV0 (BX)) and HW (BY ) (or HW0 (BY )) be the weighted Fréchet spaces of holomorphic functions. In this paper, we investigate the holomorphic mappings φ : BX → BY and ψ : BX → C which characterize continuous weighted composition operators between the spaces HV (BX) (or HV0 (BX)) and HW (BY ) (or HW0 (BY )) . Also, we obtained a (linear) dynamical system induced by multiplication operators on these weighted spaces. Department of Mathematics and Statistics, College of Science, Sultan Qaboos University, P.O. Box 36, P. C. 123 Al-Khod, Sultanate of Oman E-mail address: [email protected] Date: Received: 12 October 2012; Accepted: 17 December 2012. 2010 Mathematics Subject Classification. Primary 47B33; Secondary 47B38, 47D03, 37B05, 32A10, 30H05.