  We study multiplication operators on the weighted Banach spaces of an
infinite tree. We characterize the bounded and the compact operators, as well
as determine the operator norm. In addition, we determine the spectrum of the
bounded multiplication operators and characterize the isometries. Finally, we
study the multiplication operators between the weighted Banach spaces and the
Lipschitz space by characterizing the bounded and the compact operators,
determine estimates on the operator norm, and show there are no isometries.
