Abstract
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 ℒw be the set of functions f ∈ 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 ℒw and provide operator norm and essential norm estimates. Furthermore, we characterize the bounded and compact multiplication operators between ℒw 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.
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