Multiplication Operators between Lipschitz-Type Spaces on a Tree.

Let L be the space of complex-valued functions f on the set of vertices T of an infinite tree rooted at o such that the difference of the values of f at neighboring vertices remains bounded throughout the tree, and let L_w be the set of functions f ϵ L such that ∣f(v) - f(v-)∣ = O(∣v∣^-1), where ∣v∣ is the distance between o and v and v- is the neighbor of v closest to o. In this paper, we characterize the bounded and the compact multiplication operators between L and L_w and provide operator norm and essential norm estimates. Furthermore, we characterize the bounded and compact multiplication operators between L_w and the space L^∞ of bounded functions on T and determine their operator norm and their essential norm. We establish that there are no isometries among the multiplication operators between these spaces. [ABSTRACT FROM AUTHOR]