Multiplication operators on the iterated logarithmic Lipschitz spaces of a tree

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.

References in corpus (2)

• Multiplication operators on the weighted Lipschitz space of a tree
• Multiplication operators between Lipschitz-type spaces on a tree

Cited by in corpus (6)

• Discrete Analogue of Generalized Hardy Spaces and Multiplication Operators on Homogenous Trees
• Composition operators on weighted Banach spaces of a tree
• Multiplication operators between iterated logarithmic Lipschitz spaces of a tree
• The differentiation operator on discrete function spaces of a tree
• Multiplication operators between discrete Hardy spaces on rooted trees
• Composition operators on Hardy spaces of the homogenous rooted trees