Abstract
We introduce a class of iterated logarithmic Lipschitz spaces \({\mathcal{L}^{(k)}, k \in \mathbb{N}}\) , on an infinite tree which arise naturally in the context of operator theory. We characterize boundedness and compactness of the multiplication operators on \({\mathcal{L}^{(k)}}\) and provide estimates on their operator norm and their essential norm. In addition, we determine the spectrum, characterize the multiplication operators that are bounded below, and prove that on such spaces there are no nontrivial isometric multiplication operators and no isometric zero divisors.
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The research of the first author is supported by a grant from the College of Science and Health of the University of Wisconsin-La Crosse.
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Allen, R.F., Colonna, F. & Easley, G.R. Multiplication Operators on the Iterated Logarithmic Lipschitz Spaces of a Tree. Mediterr. J. Math. 9, 575–600 (2012). https://doi.org/10.1007/s00009-011-0157-1
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DOI: https://doi.org/10.1007/s00009-011-0157-1